I've always taken it to replace the entire lower limb from the elbow down, so no hand. But now that I'm thinking about it, I can't really see any possible reason that any person would buy such a thing instead of just using a hand-held version... it would be more expensive and allow you to do less. In light of that, I think I'd probably let you have the hand.
Of course, like a vast number of things in the game, this depends entirely on my opinion and will vary from GM to GM.