I too am RH, but left-eye.
On handguns, no big deal. Rifles with red dots or scopes, I can cope. Open sights, like a lever gun, I've never tried.
Where I suffer is shotguns. To hit a barn, I have to shoot lefty.
This has paid off with the AR.
Recently, I took a Farnam class and as with most good trainers, he had us work on weak hand as well as strong hand. I had little to no trouble making the transition, as I have sent a lot of 12 gauge downrange lefthanded.