Airbag lights and steering wheel replacement

I talked to Black Roadster briefly last week about swapping steering wheels and wondered if a swap would kill my blinking airbag light. He said it depended on what code it was flashing. Well, it's flashing a code 34 (three blinks, pause, four blinks) right now, but I swear it was flashing a 13 a couple of months ago.

Anyhow, according to the info on miata.net, a 34 means I have a short circuit on the driver's airbag, and a 13 means the "D" sensor is on (probably a moot point since it's not flashing a 13 now). My question is this... will a steering wheel swap with the proper hub adapter kill the light altogether if it's flashing a 34, or will I have to resort to the the ol' paint-the-bulb-black method of killing the light? I don't plan on taking the dash out of the car any time soon, so pulling the computer is out of the question. My guess is that a 34 might be killed with the wheel swap, but I have no clue as to the "D" sensor - which could still be lurking in there somewhere.

Any ideas?