How do opponents of Penal Substitution explain God's declaration that He "will not leave the guilty unpunished"? In referring to opponents of Penal Substitution theory, I'm referring specifically to those who view it as a false view of the Atonement, not merely that it is incomplete (eg those who hold to alternative theories of Atonement may assert their theories are more holistic, but will not necessarily deny that penal substitution is a contributing element within them).

Consider:


  ... the Lord will not leave the guilty unpunished. - Nahum 1:3b NIV
  
  Acquitting the guilty and condemning the innocent—
      the Lord detests them both. - Proverbs 17:15 NIV
  
  Have nothing to do with a false charge and do not put an innocent or honest person to death, for I will not acquit the guilty. - Exodus 23:7 NIV


If Christ doesn't bear the penalty or punishment for our sins by taking our guilt upon himself, where does the condemnation and punishment go? What is the specific mechanism by which, a sinner can be saved from their sins without making nonsense or lies of the preceding declarations?
The following answer shall be largely influenced by my Roman Catholic faith, so be aware of such a fact while reading. With that said, here we gooooooooo!!!

Penal Substitution And Its Failures

The problem with the penal substitution theory is that it confuses many points that need distinction in order to understand the nature of Christ's sacrifice. For example, under the penal substitution theory there is a reduced consideration of the theological specifications between original sin, committed by our first parents, and actual sin, committed by the individual. The supporters of penal substitution theory simply hold that Christ died for all of our sins, and bore the punishment due to each and every sin. Another point of distinction that is necessary to make that penal substitution theory seems to overlook is the difference between satisfactory punishment and penal punishment. Satisfactory punishment is voluntary and not necessary for the individual undergoing it to undergo it. It thus earns penitential merit for the individual, a merit that by its nature has the opportunity to be shared (hence the Catholic understanding of a Treasury of Merit). An example of what satisfactory atonement theory proponents would hold to be satisfactory punishment is the punishment that Christ went through on the cross and in His death. Penal punishment is not voluntary, for it is accorded by God to souls for a sin that was specifically committed. It thus has no merit opportunity, for it is solely serving to bring about God's justice. It is penal insofar as it is necessary for the sinful soul to undergo the punishment. An example of penal punishment is the fall of man following original sin. Another example is eternal damnation accorded to actual sin that is mortal. These distinctions being stated, it might be easier to understand satisfactory atonement theory more clearly, and to specifically understand its proponents when they state that Christ could not undergo penal punishment. 

The major problem with proposing that Christ underwent every single punishment for every single sin is rather obvious; if such were the case Christ would be suffering eternally in hell right now, for the punishment of actual sin is eternal damnation. Penal substitution theory also holds, as you might have guessed, a penal consideration of the nature of Christ's sacrifice. In other words, under penal substitution Christ 'became' a sinner and 'became' the guilty in the eyes of God the Father. An obvious objection to this idea is in the fact that if Christ were to be considered a sinner in the Highest Courts, God would be divided against Himself. Christ could not justly be condemned, for as you said yourself in Proverbs 17:15, God detests condemning the innocent. Also, Christ suffering such punishment would achieve no merits anyway, since as we have discussed penal punishment brings about no merit opportunity. So the matter of Christ's sacrifice thus is not in Christ the innocent being condemned by the Father, which suggests a division within God Himself and no merit opportunity, but in Christ the Perfector of the human race offering some value to humanity that every human, bound by original sin, could not offer. Satisfactory atonement theory proponents suggest that what Christ offered is a satisfactory, or voluntary, penance for original sin. Original sin is understood to be the prison by which all mankind was (is) held, for it was (is) an inescapable inclination to commit actual sin, which condemns men to hell. While we could pay penance for actual sin, it was meaningless without the penance of the more primary matter of original sin. So satisfactory atonement theory holds that Christ offered perfect penance (which included suffering, since penance is a punishment by nature) for original sin. Since this perfect penance was satisfactory, it produced merits that could be shared by those who share a love with and for He who obtained them. Christ suffering a satisfactory punishment for original sin, which implies He remained perfect before the eyes of the Father and that He did not as such suffer every conceivable punishment for every sin, in no way takes away from the glory or power of Christ's Passion. It simply upholds the consistency of God and the coherency of sin and punishment.

I think I have addressed the verse of Proverbs that you used in pointing out that it actually supports satisfactory atonement theory more than penal punishment theory. Now on to the other two verses.

Nahum 1:3


  The Lord is slow to anger but great in power; the Lord will not leave the guilty unpunished. His way is the whirlwind and the storm, and clouds are the dust of his feet.


To suggest that this verse supports an entire theological theory is perhaps incorporating a bit of question begging. But to answer to the objection, I might note that the verse in no way specifies what it means by 'punishment', and my guess is that it doesn't mean 'punishment' in the way that is going to add up to a feasible defense for penal substitution theory. The problem with this line of argumentation is firstly in its assumption regarding those who don't hold to penal substitution theory. Most would not reject the notion that all men are punished for their sins. But we must accept the notion that not all men are punished in the way they could be, or to the full extent that they could be. But for the sake of argument let's assume that this verse is speaking of the full extent of punishment being unavoidable. The second assumption read into it by penal substitution theory supporters is what is meant by 'guilty'. The 'guilty' could very well mean those who are opposing God's will, in which case the matter becomes difficult to address how this correlates to Christ. For Christ would certainly not be opposed to God's will. More so Christians would not be considered 'guilty' because they have faith in Christ, even though they were opposed to God's will at certain points. Obviously Christians do not suffer the 'full extent of God's wrath' so long as they are faithful and justified in their deeds. So we can see with close analysis that this verse truly doesn't get past being relativistic, especially if you try to bend it to a certain position. The better biblical approach is to not pull verses out of context but rather read them as they are.

Exodus 23:7


  Have nothing to do with a false charge and do not put an innocent or honest person to death, for I will not acquit the guilty.


Again, this verse seems to resonate the verse in Proverbs that you posted. As I noted in Proverbs briefly, this verse seems to be not supporting penal substitution, for it notes that God detest condemning the innocent while sparing the guilty. How much more so is it improbable that God would detest Himself, who is the Highest Good and Innocence? The notion that He would suffer a penal punishment as though He were a sinner, at His own bidding mind you, has rather obvious problems, one such example being proven in the verses you posted. To post verses that presuppose satisfactory atonement theory I might add the following:

Leviticus 17:11


  For the life of the flesh is in the blood, and I have given it for you on the altar to make atonement for your souls, for it is the blood that makes atonement by the life 


Genesis 4:4


  ...and Abel also brought of the firstborn of his flock and of their fat portions. And the Lord had regard for Abel and his offering... 


Genesis 22:2


  He said, “Take your son, your only son Isaac, whom you love, and go to the land of Moriah, and offer him there as a burnt offering on one of the mountains of which I shall tell you."


Proverbs 21:3


  To do righteousness and justice is more acceptable to the Lord than sacrifice.


All of these verses support the idea that a sacrifice is firstly focused on the notion of offering something to God, albeit amending a debt, that is meant to cleanse us. I might also note that Cain and Abel offering a sacrifice is interesting because it only further interlinks the closeness of sacrifice (penance, punishment, etc) with original sin. It was only after the fall, and probably for the fall, that these sacrifices came to be, carried out for the old notion that we as a race owe something to God. But God does not 'require' sacrifices in a legal sense. This fact is seen in the last Proverbs verse. The nature of these sacrifices are an embodiment of the perfection that is owed to God but that is not achievable through fallen man. Thus is it that we see God being more pleased with more meaningful sacrifices; these sacrifices were predecessors to the true and perfect Sacrifice of Christ, who offered full penance in His perfection for original sin.