If a qualified right-handed welder breaks his right hand, his right arm, or otherwise unable to weld, is he also qualified to weld with his left hand? The code has limits with regards to qualifying process and positions, but not the appendage used during qualification.
Your internal quality system can implement a distinction and implement it into performance qualification testing. That would give it the authority of the code.
Qualification can also be withdrawn if welding performance is inadequate.