I'm cross-dominant -- right hand/left eye. For decades my corrected vision was good enough I could get away with using my non-dominant right eye, shutting or squinting my left, and getting rounds on target; this was comfortable for me. I get the concern about peripheral vision but think some take it to the point of the tail wagging the dog; yes it matters, but not more so or even equal to hitting what's in front of you quickly and accurately.

My vision has changed enough that relying on the non-dominant right eye isn't cutting it anymore -- fuzzy everything. What seems to be working now is adjusting my stance and grip to a Chapman, locking my strong arm and making a slight cheek weld with it, and shooting both eyes open using my dominant left eye to line things up. It isn't pretty, but bad shooting is uglier.

Don't worry about what's right, experiment and find what works well for you and be ready to adapt and evolve when circumstance necessitates.