You should be shooting with both eyes open regardless. Especially with handguns and shotguns Some people struggle to do so paricularly with a rifle and optics. Having quality glass helps.
First determine which is your dominate eye. You should be shooting from that side. It will be easier to retrain your arms and body You will not retrain your brain and eyes. Learning to always shoot with both eyes open with any gun will make you much better and cancel some of the effects of cross eye dominance.