For years when ever I used a long weapon, I always shot left handed, just seemed normal and shot pistols right handed, I have no idea why!! All way through my army career I fired all rifles and other long weapons left handed untill the SA80 came around for us and then I had to learn to shoot right handed all of a sudden!
To be honest, even though it felt odd at first, it became normal, I know it sounds odd, but if you really feel it is awkward, get a replica or make one and at home practice right handed, sounds weired and you look like a prat but, if you do it enough it becomes second nature, you have to build up the muscle memory.
Now I shoot predominantly right handed (wepon side) but I can also shoot well enough to pass all testing, support side too.
Like was mentioned, find out your dominant eye, just using your thumb as a sight use one eye then other, see which one stays on sight when you open the eye, that should give you your dominant eye!!
Best of luck to all who are going for armed response, then onto tactical, its a fantastic line of work.
Stay safe everyone