Based on the rules of the game, no a q-tip is not a finessable (god, is that a real world?), but to reason and logic it could be. Whether or not Dnd made it to be based on strength or dexterity is irrelevant, the fact is Both the wizard and the monk gain proficiency with it, and the monk uses it differently then ye olde man of arcane lore.
I think for a monk it should be allowed, but for anything else (except maybe for a Shaman from OA) it should not be allowed. In fact, I think it should be a monk abiity to replace his str bonus with his dex bonus with some of his weapons, q'tip included.
I think Dnd fails at incorporating both western ideas of the staff, as an "old man's walking stick" and "pupil disciplinary tool", and a deadly poker of the eastern monks.