I tried something similar to that, but received an error message. What I tried was using an aim constraint on the wrist joint, and using a locator as the target. I didn't quite understand what the issue was, but I assumed that it had something to do with all the fingers being selected as well due to the parenting when I selected the wrist, and I must have had too many contrained things.

I'll try the orient constraint tonight. Is there something I need to do to select only the wrist without Maya automatically selecting the rest of the chain, or can I just select the wrist as the constrained object and Maya will be OK with the rest of the chain being selected as well?