I've shot thousands of rounds through various right-handed shotguns. The vast majority of them have been through half a dozen or so different Model 870s, with the majority of those being my own Wingmaster. I've also shot a couple thousand rounds through a Benelli M1 Super 90, a couple different M1100s, and a Winchester M1300. I can't recall ever having a single hull hit me in the face.
Interestingly enough, my fingers are long enough that I don't have problems manipulating the controls either. Even the cross-bolt safety on the Rem isn't a problem for me. In fact, my brother, right-handed, gets a run for his money when we shoot trap or take the shotguns out ground squirrel hunting.
I am right-handed but left eye dominant. I find this arrangement can actually work out quite well. My strong hand is the support hand so I find I can hold the weapon steady and track with greater coordination. But it does mean that I've had to learn to adapt. Pump actions, semi autos, and lever guns are fine. Bolt rifles are the only weapons I insist be left handed, and even then I can and have used righty weapons, I just prefer the lefties.