OK's laws concerning transporting a handgun in a car without a CHP are the same as other guns. It specifically says in section 21-1289.13 of the law code that you can't have any loaded firearm in a vehicle, unless it's a handgun and you have a CHP, or if it's a rifle or shotgun, the chamber's empty, and it's in the trunk. So if you were desperate to have a shotgun ready to pump in the trunk, you could, but anything in the passenger compartment has to be totally empty.
However, it's not completely hopeless. 21-1289.7 allows you to carry any pistol, rifle, or shotgun anywhere in a car, if it's openly visible and completely unloaded. "Completely unloaded" means "clip unloaded" as well; it's unclear if that means you can have a loaded magazine separate from the gun itself, as I could find not governing court cases setting a precedent, but I'd bet that you'd have to explain yourself if a bad minded cop felt like hassling you.
Oklahoma will probably be the worst leg of your trip for protecting yourself in your car, alas, but enjoy the country in any case!