Introduction: Become an Ambidextrous Computer Mouse User
Simple really: practice! :]
Seriously though, RSI due to computer mice is no joke and I've suffered from it myself.
In one desk job I had some years ago (mapping city council park assets), I had such a problem with RSI that I investigated several mouse options, eventually ending up with the joystick-type 3M Ergonomic mouse in ewilhelm's "Ergonomic work station" Step 5. The main problem with this was it uses the bigger muscles of your arm so I found it difficult to easily get the fine movement control I needed. Way before even that, though, I'd bought a Genius Trackball which I loved. Other family members didn't though...
Step 1: Train Your Other Hand
What I've done in recent years is simply train my left hand to use a right-handed mouse (ie left click with my left middle finger, and so on). This is so natural now that I can swap the mouse from side to side of the keyboard as if I was ambidexterous. This has resolved the RSI issue for me, and I can highly recommend it. It doesn't take long to get the hang of using the "wrong" hand fingers to operate the mouse.
It also means that you don't need to swap the mouse button functionality for each side of the keyboard, and other people can use the mouse as normal. AND lefties can use other people's mice.
I now play Deus Ex right-mouse with the left hand operating keystrokes, and browse the Net (eg Instructables) left-mouse so Page-Up etc are controlled with the right hand. An added advantage is mousing with the left hand while number entering with the right (so you don't have to keep shifting your right hand from number-pad to mouse), and wordprocessing left-mouse so you need not reach so far for the mouse.