I don't want to clean guns or load ammo over a carpet that will hold spills.
My present shop has rubber tile like you see in gyms with a hard plastic desk chair liner at my most used press.
I would not open a door back into the house for ventilation, open a window.
I would (Do, even in a shop opening off the garage.) clean with M-Pro 7 which is a detergent rather than a solvent. It is not flammable and has almost no odor.