Happen to (in questions) I'm aware that you can use 正好 or 碰巧 to express low probability in statements, equivalent to English "happen to" .

我正好是有你要的那种啤酒。

我发现他碰巧就是我的一个远亲。

How can you use this same idea in a question?

"Do you happen to have an eyeglass screwdriver?" 

Edit: I want to express that I'm aware the probability of them having the [unusual item] is low, but that I'm asking anyway.
Normally you wouldn't translate happen in questions like the one you proposed.



But, if you really wanted to - the best equivalent I can think of for doing this would be by adding:


  顺便问一下


at the beginning of a question.

So your question would end up being something like:


  顺便问一下，你有没有眼镜护理螺丝刀呢？