YOu are probably going to have to roll your own. Use a piece of dowel rod the correct diameter for the work. If you consult the " Drill Bit Chart " for making ball blocks, you can find a drill bit size for most of the shot gun gauges. A .550 barrel is 28 gauge, so use a .50 caliber rod, and a half inc dowel, or the shank on a 1/2 inch drill bit to serve as your mandrill to roll the cups.
A 20 gauge is .615, so drop down to .58, or 24 gauge for wads, and find a drill bit that will cut that diameter hole. A 37/64" bit should do the job.
For a 16, ga, drop down to 20 gauge for the wads, and use a 5/8" diameter drill, for the mandrill.
For the 12 gauge, use a 14 gauge wad, and a .68", or 11/16" diameter drill for your mandrill. The Dime coin wrappers are very close in size to this requirement, and you might save yourself time by using them instead. I have not tried to see what size wad they will take down them, so check that out before buying many of them. They are available from Stationary supply stores.
I have tried Index card stock, newsprint, grocery sack, and 3M Post-It note paper, and I found the most convenient paper was the Post-It note paper. The good news is that it comes with a self adhesive strip on one edge, saving you the messing around with glue. I tried one circle of the paper, and created instant confetti. I tried three wraps around the mandrill and created a shotgun slug. Th en I settle on the compromise- 2 wraps-- and that seems to be working well. No holes showing that the shot pellets are rubbing through, as you some times see with modern plastic shotcups. As long as I don't let any of the paper fold over the top-- I use an OS Card to hold the shot in the barrel --- I don't get the " slug effect". I am now trying to see if I can affect my patterns to any measurable extent by cutting slits in the top of the cup, to form " petals" just like those that appear in modern shotcups, but by varying the depth of the slits,( and therefore the length of the petals) I hope to control when the shot is released from the cup in mid flight, and improve patterns down range.