I tried using a mouse in my left hand in left handed mode back in the day. Eventually, I got tired of changing the settings on shared computers at home/school, and I realized it wasn't any more or less hard to use the mouse with my right hand. Today, I use a right handed vertical mouse. Interestingly, I play guitar right handed, despite being inspired to play by Kurt Cobain. My girlfriend got me left handed scissors as a joke, but man, they actually feel better.

My sister used to use a neutral mouse, with her left hand, on the left side of the keyboard but in "normal" or "right handed mode". Now she has a laptop with a big touch pad in the middle.