My left-handed daughter (of 5) has been using the mouse right-handed all her life (!). As it was a totally new skill to her, I don't think it mattered to her which hand she learned with, but I think that being able to use it the way 99% of offices will be set up will be beneficial in the future.
I think some skills are learned, e.g. the mechanism of writing, drawing, using a mouse, so you can learn with either hand, whereas others are instinctive, e.g. hand-eye coordination, in which case your good hand will lead you. No doubt the old dog adage applies to those of us who learned mouse skills etc. later in life - hence the problems lefties have with mouses in badly set up offices!