If it has a propeller-type blade, it is an axial fan
If it has a squirrel cage, it is a centrifugal fan.....swamp coolers have centrifugal fans and the fire dept uses a centrifugal fan to clear the smoke......better for your application.

Renting one is a good idea since you save money but also can rent two if the fumes get too bad.

Can you make CHR your beneficiary on the insurance? (just in case)

By the way, we've all probably painted a car using less than perfect safety conditions.....I gave up the garage idea because I couldnt get enough light over the entire car surface. Before you go too far, you might want to set up your lights to see (!!) what it looks like.