I am left eye dominant and right handed as well. With a rifle, I shoot right handed because it feels comfortable. Duck hunting, I shoot right handed so that I don't get a cartridge in the cheek. Upland hunting, I shoot both right and left handed depending upon where the animal flushes from and which way is faster.

That said, with a new shooter, I would teach them to shoot on the appropriate side in relation to their eye dominance.

Good luck,