I do not believe that cross dominance is a function of the acuity of the vision in each eye. If you wear eyeglasses, the acuity should be nearly the same in each eye.
I have worn eyeglasses for nearly 44 years, and had closely matched acuity, but still have a cross dominance problem. One of the doctors I have seen commented about how strong my cross dominance is.
Changing eyeglasses or having laser surgery will most likely NOT affect your cross dominance. Vision therapy may have some chance, but I wouldn't expect that your rifle & pistol shooting will improve from it, but maybe shotgunning will improve.
I gave up on shotgunning with my eye cross dominance, since I shoot from the stong-hand-side shoulder. I have noticed just lately that I am shooting pistol with my dominant eye from the strong hand side. Before my surgery for a detached retina in my non-dominant eye, I used to shoot pistol with the non-dominant eye. I still shoot rifle with my non-dominant eye, but my eyesight now requires use of a scope in order to see the target and the sights. Bi/tri-focal eyeglasses do not work well with iron sights on a rifle.
If you want to shoot flying targets with a shotgun, get some good training from a qualified instructor to help you learn to shoot using the shoulder that matches your dominant eye. That will cure most of the problems with lead changing depending on which direction a crossing shot is originating from.
Learn to shoot handguns with either hand, and let the eye dominance sort itself out (don't worry which eye is lining up with the target - just focus on the target and bring the sights into the line of sight - if your wrist is cocked and you still hit the target, who cares).
Get a scope on your rifle if you don't have one, and the eye dominance is a non-issue.
I have been shooting for many years with cross dominance, and except for the shotgunning matter, it has had insignificant affect on my enjoyment and ability to hit what I aim at.