Can a Wizard use his charm ability with no cards in the hand?
No he can't, although official evidence is a little circumstantial. This question is in an old version of the Munchkin FAQ (but not the current one):


  Q. A wizard must discard his hand to use his charm ability. Can he do 
  this if he has no cards?
  
  A. No. If you have no cards, you don't have a hand.


This is corroborated on the Munchkin wiki:


  You can't use the wizard's abilities if you don't have any cards in your hand.