I am right handed/left eye dominant and shoot all firearms right handed.

For pistols I just move my head slightly to the right. For rifles I close my left eye and for shotguns...... well lets just say I don't hit too many flying targets. I tend to just close my left eye and sight along the rib. My semi-auto 12 gauge has open sights though.

I have an additional problem too. I was born myopic and with astigmatism. Laser surgery in the mid 90's mainly corrected it but I am +1.5 in my right eye and - 1.5 in my left. As I have gotten older my vision has tended to alter too, so while I can just about clearly see the front sight on a pistol with my right eye it is hard in my left. I finally got around to getting some eye glasses a year ago, however while the prescription is great for anything slightly further out that the front sight of a pistol it just won't work with a pistol!

I have worn soft contact lenses when driving for a few years now and these are great, I can see the front sight perfectly, but early this year I travelled to a level 2 IPSC event and tore my left contact lens taking it out after the first day. I shot the second day using my right eye and once or twice forgot to "switch eyes". (Lesson learnt, always take spares of every thing. I am thinking of getting a new prescription lens for my left eye that focuses at pistol front sight distances and gluing it into my shooting glasses. We'll see.

The contact lenses are also the answer for CAS rifle shooting when I can't use a scope. And as for work, well that's why I went to contacts in the first place so the red dot sight on the M4 works well if I squint my left eye closed slightly. And many years ago I shot a qualification shoot with a S&W M10 .38 Spectial left handed and did better than I do right handed. Have never been able to duplicate that again though.

Personally, I don't think there is a "right" or a "wrong" way when you are cross eye dominant. Find something that works for you.