RE: shotgun/ left eye dominant
I have found that over time, I have automatically compensated for being wrong eyed (right handed/left eye dominant). That said, if my son is left eye dominant, I will start him right off shooting left handed.
I think it's a great idea to look at the O/U or even Side by Side option; or even single shot. That way, if every he wanted to shoot right handed, despite his strong left eye, you/he won't have to buy a new gun.
Good luck