I'm a lefty through and through in my sixth decade going around the sun. Mousing with my left hand is weird. Like completely wrong. Even on a touchpad I tend to "mouse" with my right hand.
Some lefty's do. I use the mouse right handed and even hold a guitar right handed. Some things you just train yourself to conform to society with. Kind of a shame I'm not an artist because I can have an amazing setup with a drawing tablet, keyboard, and mouse that is all at my beck and call.
(and... that, with my off hand as well. No clue why. I guess I hold a screen with my dominant hand?).