I am right eye dominate and shoot right handed, I shoot with both eyes open with iron sights with flip up blinder over my left eye. When I shoot skeet I shoot right handed with both eyes open.
I know a few very good shooters that shoot the opposite hand because of cross dominance. First shooter, left handed in everything, hockey, lacrosse, baseball, writing, right eye dominate, shot right handed. Made several Bisley teams, Canadian Olympic Smallbore, several Palma teams shooting right handed.
Second shooter, right handed, left eye dominate, shoots left handed. Made about 30 consecutive Canadian Bisley teams, Palma teams etc.
Shooter number 3, right handed all the way. After many years shooting right handed now has vision problems with his right eye. Still shoots right handed with offset iron sights. Made more Bisley teams and Palma teams than I care to count.
Bottom line is, shoot with your dominate eye.