From experience, a lot of people tend to shoot as--or more--accurately with their non-dominant hand if shooting one-hand-only. They may shoot a little slower, but a lot of it has to do with the newness or unfamiliarity of it...automatically forces more concentration on sight picture and trigger pull. This is a similar phenomenon to one that causes embarrassment of grizzled guys who "have owned handguns forever" (but who don't really train or practice all that much), when a young woman who is just learning to shoot stands next to him at the range and repeatedly punctures the X-ring.
Are you going to have to buy a left-handed holster, as well? If so, and if you don't already have a BUG (and considering that the dominant-hand downtime is going to be relatively brief), I think I might want to consider looking for a pocket pistol that could continue to see future service as a BUG carried in the front left pant pocket.