I can do anything, save throw a ball, with either hand. I prefer to use my right to shoot because that arm is stronger, especially since I separated my left shoulder (On the left-hand-only part of IDPA, it looks like my 9mil is a .44 Mag.). I'm naturally right handed in everything, but I have taught myself to be nearly ambidextrous. I can also temporarily focus primarily with my left eye even with both open.

I've a friend that shoots right handed with his left eye. Perhaps that would work for you. I'd suggest doing whatever feels the best to you.