I would probably ask his Orthopaedic doctor for advice. The only ride that really comes to mind for me is Rockin' Roller Coaster because it goes upside down, maybe Everest, too. You might want to put a plastic bag over it on Splash or Kali so it doesn't get too wet.
I would ask the doctor because he knows how th arm is healing. Also, is he able to hold on with that hand, or is the hand part of the cast?