As a lefty I never had any problems adapting to a right hand mouse and actually find the keyboard to be better suited as a "left hand" activity and would have a hard time switching it up.
I'm a lefty, but always mouse on my right (keyboard left). This has made me exceptionally good at using hotkeys, to the point where a friend at a LAN party called me a hot-key whore. He wasn't (and still isn't) wrong. After using any program for a while, I will figure them out, including how many times to press tab to get to a field.
Living with laptops with touchpads for a couple of decades as a righty, I can use a touchpad perfectly fine with either hand, but a mouse is still right handed for me.