Can K + N vs K force black into any corner? Can white force this position

    [Title "KN vs K"]
    [FEN "8/8/8/8/8/8/5k1N/7K w - - 0 1"]


into this position?

    [Title "KN vs K"]
    [FEN "k7/8/1K1N4/8/8/8/8/8 w - - 0 1"]


Background:
Yesterday I finally figured out the KBN vs K after one year of trial and error. Solving endgame problems like this is like crack to my brain. The 'fifth' fundamental checkmate and next in line seems to be the KNN vs KP. 

In this game, one of the Ns only play a passive role, with the other N and the K are doing all the moves, I started wondering if the same approach is possible in the KBN vs K: Force the king to the corner with only K and N, and then deliberately deliver the checkmate with on B's first move.

Any concrete suggestions that could lead to an answer will be greatly appreciated.

A related question: is there an engine that can search for such non-checkmate positions?
I am not aware of being able to use an engine to calculate the possibility of such moves and no it is not possible to do this with one knight.

The easiest way to figure this out is by backtracking the position by one or two moves. No matter in which position the white king or knight were before this situation arose, black was not obligated to move to the corner of the board.

1k6/8/K2N4/8/8/8/8/8 w - - 0 0


black can move to C7

8/k7/2KN4/8/8/8/8/8 w - - 0 1


black can move to A6

8/k1K5/3N4/8/8/8/8/8 w - - 0 1


black can move to A6 here as well

2k5/8/1K6/1N6/8/8/8/8 w - - 0 1


And Regardless of the position of the Knight the black king has a square on D8 to go to.

The only way to actually get this done is if the king was in the corner to begin with:

k7/8/1K6/1N6/8/8/8/8 w - - 0 1