Hey Josh,
it may take some getting used to, but you can do it. There's several different approaches to this that you might want to consdier. A crossover stock is one, offset sights or scope bases are another. If you haven't seen these before, the crossover stock is one that looks like it's been run over by a truck. The butt stock is bent offset enough to allow the new dominant eye to do the sighting. I've seen these use a lot by shotgunners, and they're fairly common there. Among highpower shooters, offset sights have been used for year. They're exactly what they sound like; the sights (both front and rear) are set off via a base, again to allow the dominant eye to be used for sighting. Had a friend who did this after being partially blinded in a shooting accident. In addition, something else you might want to consider; the NRA and CMP both have several programs for disabled shooters, and some specifically for wounded warriors. I shot next to a bunch at Perry this year, and I' gotta tell you, it's pretty damned inspiring to see a guy with no legs shoot standing, and do well with it. There's several different types of shooting events that you may consider, and some may be easier for you than others. A friend of mine, Bob Depp, recently started shooting F Class after having not shot for many, many years. Bob suffered terrible wounds in a "friendly fire" artillery incident at Khe Sahn and was originally told he'd be a quadraplegic for life. He's back out on the range shooting again, and having a ball. He still has one arm that's almost useless, but this particualr type of competition is very well suited to him and it gets him shooting again. Bob has been involved with (runs) an organization for wounded Marines for many years, and would be worth chatting with. Let me know if you need any additional info, or would like to be put in touch with any of these organizations. Glad to help, and we'll see you on the range.