I've had to deal with a number of cross dominant shooters.
Firing pistol, not a big deal.
Firing rifle, potentially a problem. Especially if you try leaning over to use your dominant eye with your opposite side.
Pistol shooting, fire with both eyes open, and things will work well.
Rifle shooting, well, something I've seen done is to place a piece of 'magic' or 'scotch' tape over the dominant eye, forcing you to use the non-dominant eye when using the rifle.
I recommend you identify this to your training staff when the time comes, and they will help with this.
NS