I write and do all other stuff requiring dexterity with my left, but I use my right to operate a mouse. I can use my left as well, but I learned to use my right hand for convenience.
I very rarely see a right-hander who can do the same.
Strangely I find my right to be more accurate but could be down to the extra concentration applied (particularly playing sport). You can seriously mess with a batsman in cricket if you can bowl with the right and then switch to left.
Inigo: I admit it: you are better than I am!
Man in Black: Then why are you smiling?
Inigo: Because I know something you don't know.
Man in Black: And what is that?
Inigo: I am not left handed! [switches the sword to his right hand and starts driving him back]
I can have a pencil writing notes in my left hand, while I control the computer via mouse in my right.
Similarity, mouse the cursor with my right and type with my left.