Okay, so why would I not want a wand to perform these spells?  Like… is the point to be super sneaky or something?  I guess I don’t understand this question.

How about this: if I didn’t have a wand, I’d want to be able to perform Expelliarmus sans wand.  That way I’d win a wand and have the ability to cast all those other spells that require a wand.  Ha.