Tim, Try different paper types and different thicknesses. Paper cups work for some situations and not for others like most muzzleloading stuff. I have a non-choked .62 smoothie and compared to no shot cups, it gives a much better pattern and for longer distances with the above mentioned sticky note paper cups (gaining 7-10 yards consistently over no cup).
I was fortunate almost 20 years ago to have Mr. Lowell Tennison (sp?) jug choke another .62 smoothie barrel for me. At the time he was the GO-TO guy for jug choking. If this is what one wants, I believe there are currently folks on this forum that perform excellent Jug chokes. I asked Mr. Tennison to jug choke the barrel to "Super Full" for squirrels and Turkeys. I have 100'-120' tall mature oaks, hickories and other hardwoods on my property where I need the extra tight pattern to reach topped out squirrels. This Tennison jug choke outperforms my modern stuff with lead shot (Chilled or magnum lead shot). I will shoot at and kill squirrels at 50+ yards.
All that said, working up paper shot cup combinations in the non-choked barrel allows me to keep tight patterns for medium+ range (25-35 yds) squirrels and turkeys. The paper shot cups do need to split and/or burst upon powder ignition but they hold together long enough to protect the shot and the bore from any leading. One has to work up the best shot cup loads for your barrel/gun (paper type, thickness, wrap count and lube/no lube) just like any other shooting combination. It may or may not work for you.
If one is to stay completely traditional, one might want to avoid the shot cups or anything non-traditional. I like flintlocks and blackpowder shooting but do not limit myself to completely traditional components. Do what works for you and your traditional/non-traditional conscience. I have taken most all game in my area with traditional muzzleloading and other primitive weapons. I use my methods now to keep this decrepit body out hunting and enjoying the sport.
Above all, enjoy what you are doing!
Respectfully,
Dan