Many years ago, one of the gun publications printed an article regarding the "Quell Method" of shooting. It encompassed the dominant left eye of right-handed shooters. I wish that I had held onto that article, so that I could send it to you.
Basically, the "Quell Method" consisted of USING the dominant left eye for aiming while still shooting right-handed. With ANY firearm, you would need to angle your head (either dropping your right cheek on your right arm when shooting a handgun, or placing your right cheek on the stock of a rifle, so that you can aim with the left eye).
I was taught as a "rightie", but I began practising as a "leftie" as well....and that included the eye to aim with. Through experimentation, especially after reading about the "Quell Method", it took some time and a LOT of pracise to become proficient as an "ambidextrous" shooter. It CAN be done, and after you've mastered it, it isn't all that awkward. (HMM! I still look like a girl when I try to throw a ball as a "leftie"!)
Lastly, and whether you believe it or not, shooting and hitting a baseball have several things in common. The baseball bat is merely an extension of your "batting" arm, even though both arms are used.
You can "place" a baseball where you want it if you know how to use that "extension". Add to that, numerous baseball players, who are "righties", switch over to batting as "lefties"....and actually increase their batting averages! It's done through PRACTISE, PRACTISE, PRACTISE! It may seem awkward for awhile, but.....!