As I understand it, the amount of molecular oxygen available in the cartridge case from air is negligible. The "oxygen" in smokeless powder is provided through an oxidizing agent, namely the nitro groups of the nitrocellulose which accept electrons from the carbon of the cellulose portion of the nitrocellulose. This is similar to molecular oxygen accepting electrons from the fuel in open air combustion of fuels. In black powder, the fuel is the charcoal (carbon) and the oxidizer is the potassium nitrate.
