It is difficult to shoot handguns if you are cross dominant. Most folks will tell you to keep both eyes open when shooting any gun at all, even scoped rifles. I think that is bad advice for anyone who is cross dominant.
Shooting with both eyes open is ostensibly done so that the "aiming eye" sees a bit better. That, and under most defensive (and hunting) situations, we need to see as much as we can possibly see. That's all well and good, unless you are cross dominant.
I do most of my shooting with my left eye closed. Even when hunting. Having never been engaged in a self defense situation, I cannot say one way or another how that would work out. Otherwise, having my left eye shut has worked for me. I have two grocery bags full of medals and a shelf full of trophies that would seem to indicate it works o.k. for me...
I would just go ahead and close your left eye. Forget the naysayers who claim that is "not how it's done". We need to be able to adapt for our individual needs.
And, god dammit, if you put a laser on that Vaquero I'll drive all the way to Lacey... Don't make me drive all the way to Lacey...