Whenever I begin to worry about Carpal Tunnel Syndrome due to pain in my right arm/wrist, I switch to mousing with my left. I've been mousing with the left hand for the last few months, in fact, and at this point I can't even remember having had any difficulty in adapting. Otherwise, though, I find it extremely awkward to attempt to change the performance of routine actions from one side of the body to the other:
I always hold the phone in my left hand against my left ear
place my right leg into my pants first
brush my teeth with my right hand
If you're feeling the need to swith hands because of pain, just keep at it: you will very soon have trouble even remembering that it was difficult at first.