Free: Contests & Raffles.
As long as you do not have the .22 ammo on you, you are legal.
If you have a gun with a shotgun barrel loaded, and a 22 rifle barrel that is not loaded, it should be obvious that you are hunting with a shotgun. I can't imagine any warden writing someone up for that. What if you want to carry a 22 pistol while turkey hunting with a shotgun? Just because you have a handgun strapped to your belt does not mean you are hunting with it.
I was checked last year while duck hunting, the warden had me unload, then ran some sort of wand over my shells to chech lead free, then had me reload and check if I could put a third shell in my benelli's tube. This was all after she walked right through my spred and freaked out my dog.