Comment by contravariant

It's probably more like "You wouldn't happen to have any X?". I assume the idea is that you put the emphasis on the asker being the one to ask a silly question if they indeed don't have it.

Maybe it also helps that all the sentence markers that make a sentence polite, negative, interrogative all get added on to the end (to the verb) in japanese, which probably makes the construction slightly less awkward. In this case it may go something like motsu (to have) -> mochimasu (to have, polite) -> mochimasen (to not have, polite) -> mochimasenka (to not have, polite, interrogative).

I'm making a lot of assumptions here though, I don't know if this is anywhere close to correct.