Hardest part of hunting deer with a shotgun, is sucking it up and paying good cash out for ammo.
Buckshot for up close, slugs for distance as far as you can reliably hit a kill zone with. Sabot slugs for rifled barrels, 'rifled' slugs for smoothbores. Practice!
Slugs from a shotgun work very well. Lots to be said for a big heavy bullet, moving slow, as far as terminal effect is concerned, and you don't get a pile of bloodshot meat, either.
Lots of good Shotgun/Muzzleloader only zones in SK. IIRC it used to be a month of Archery, and Month of Shotgun/ML, then a month and a bit of Rifle season for deer. Made for a long hunting season with lots of opportunity to get out!
Cheers
Trev