The best remedy is to switch your gun holds to the side with the dominant eye and then proceed from there. For those that have a real problem with changing over from their strong arm/hand to accommodate their dominant eye, this is one thing I've heard that can help. A piece of tape is placed over the shooting glasses on the dominant eye side. This does not completely occlude the vision, just obscures it enough that the weaker eye takes over.
This method works, when the glasses are used, and often the weaker eye is trained well enough that the tape no longer becomes necessary. The big draw back to not switching over to the side of visual dominance, is that during instinctive shooting situations the strong eye is liable to interfere.
Wing shooting with a shotgun will be difficult unless the dominant eye is obscured. In a real SHTF situation where point shooting occurs, with a handgun, not learning how to use that strong eye could cause some aiming difficulties.