if you are going to reuse the seat, it's best to remove the module. (explosive and whatnot.) Don't really want that in your house.
but, it seems you are in luck, I've recently written off a car where it had multiple airbag deployments. (seats, curtain,dash, leg bolster, and steering wheel...about 5,000 bucks worth of just airbags in all not to mention the car itself... so, write-off!)
the "seat" airbags are pretty small (a little larger than your foot when inflated) it's mostly to bolster your hip down and over into the seat to keep you in place when impacted from the side so you don't drift up and over out of the seat and into the door during impact.
"side curtain" come down from the roof from a separate module.
anyways, I digress...depending on the construction of the seat, you may be able to uzip/unhook/unclip the cover from the backrest portion of the seat (at the bottom) and pull it up to access and remove the airbag module.
just fill it with something (padding etc) as not to cause a dent in the seat side due to the void and pull the cover back down.