Look kemosabe, there should be no such thing as 'weak handed' shooting. Is there 'weak handed punching'? There is only an out-of-practice hand that you have failed to practice with.
Learn to shoot with either hand. Start with a 'red' ASP gun for all your drawing practice with your out-of-practice hand. Then a .22 and build up the skills.
Why?
Never know when you will injure one of your hands, or shoulder, or fingers, or simply have no choice but to use that hand due to unavailability of the shot is easier from that side.
You will find you don't even need to shoot as much with that out-of-practice hand cause your more practiced counterpart will transfer some of the skills it has to the other one.
Deaf