I've used right handed mice for general stuff, but when it comes to precision gaming I simply don't have the pinpoint accuracy required for a lot of things, especially shooters. Something with big buttons maybe, but even that takes a while.
My right hand actually performs well on the keyboard - I use my pinky finger for most everything outside of the arrow keys and hotkey the numpad.
If notice a larger majority of lefties have adapted to use their right hand for mouse work - I have alway's envied them - maybe this will begin the revolution back to our natural ways!