I'd learn to shoot righty.
I'm not a southpaw but both my parents are and my ex wife is. My dad was left eye dominant but my ex was right eye. She would cock her head to the side when holding a pistol and aim with the right eye.
From both parental and other experience with lefthanded people in a righthanded world, it's usually just easier to do things righhanded.
I think I've heard some studies show that left handed people have a generally easier time being ambidextr-- ambidexter-- using both hands or switching to righthanded than righthanded people have doing things lefthanded.
And from experience with my dad (born crosseyed, now eyes point at an outword angle) and a girl my mom babysat when I was growing up (lazy eye), retraining your eyes can take years and years of work with an eyepatch and generally only 'sticks' if you start young enough.
Besides, like a lot of things, guns tend to come mostly righthanded and the ones that are lefty tend to be more expensive.