I grew up in the KC area, literally in a sporting goods store, and we lived on the Kansas side. As a result, I had dual residency, and didn't have to have an out of state license in Missouri. That was good, but from a hunters standpoint, the seasons in both Kansas and Missouri are quite lacking, even today!
First, you'd best check the rules about what you can and can't shoot with an airgun as both states are behind the times. The same goes for small game, because there are still seasons for rabbit, squirrels, and other similar small game.
Here in New Mexico, there are no closed seasons for most small game (squirrels, coyotes, rabbits, hares, skunks, and about a dozen others), and airguns are allowed as well. Feral pigs aren't protected either. And, if you're interested in big game, Himalayan Tahr are unprotected (except for one county), and you can use an airgun for them too, but it should be a big bore (≥357).
So drive about a thousand miles, buy an OOS license ($75), and enjoy the hunt!
