When I was in the army I switched to holding my assault rifle right handed because I was near sighted on my left eye. (Not getting the casings ejected onto my right arm when they later gave me an LMG was an added bonus, man that gun was poorly designed)

It took maybe a week to get used to the switch but wasn't that big of a problem even though I'm both left handed and left eyed.

So you just.. do it, I guess?