I think you are full of wishful thinking if you think that your going to hurt yourself shooting coyotes with a shotgun..
No offense, but new hunters generally don't shoot more than 20 or so at best. The first year i hunted i only got one.
Shooting Coyotes close (within 50yrds) with a rifle is harder, especially if they are moving. Not to mention they mess up the pelts and in Kansas, i would want to make sure I take the highest percentage shot possible and not ruin pelts within 50yrds. I like the modified choke and Hornady Coyote shells for the price and quality.
New hunters, generally shoot farther at coyotes. The better you get at calling and hunting, the closer the coyotes are going to get and the more you will shoot with the Shotgun. Taking them with a shotgun is usually a reflection on the quality of your stands, paying attention to the wind, and the quality of the calling.
I would be really happy if i shotgunned all of my coyotes in a season. There are going to be cases where you need to make a running shot, and also long shots for those stubborn, or run off coyotes, but overall, count the ones that come into that close ranges as good success.
Just my opinion. good luck.