Call me chicken if you want, but I'd at least pull the back seat, the quarter panel cover, and roll the carpet back. Sometimes there is a lot of old seam sealer around the wheel wells, if that stuff catches fire, you need to put the fire out quickly. If there are seats or interior panels still in place, it will slow down the fire extinguishing action.
When I weld on a car, I have one of those $2 plant sprat bottles I fill with water I have beside me, and a big fire extinguisher sitting close by. That water spray bottle has saved my butt many times and is much easier to deal with then a used extinguisher.
While your welding, if something looks, smells, or sounds "funny" stop welding, pull off the helmet and look for a possible problem. If a fire starts inside that car, you have about 30 seconds to put it out before it gets out of control. Stuff inside cars tend to self feed a fire, they grow pretty quickly. Water first, if its still burning, the fire extinguisher, if its still burning get the car out of the shop, and/or get away, while you call the fire department! When the fire is burning inside a car for 20 seconds, it can do $1,000 (or more) damage to a car. Been there, done that! Gene