I'm completely confident you could make a shot cartridge in near any straight walled cartridge.Per the old speer shot cap reload data, lower pressures are better, and patterns are worse as pressure increases.
44-40 could work, but its almost not a straight wall. I think 38-40 could be troublesome, keeping the bottom wad straight. 45 colt? Sure. Absolutely. You could make them for 38-55, 375 Win, 357 Max, 454 Casull, etc. And I think 45-70 would actually be semi decent since you could get a boat-load of shot in the thing........ You aren't going to find shot caps (which are only a speer product) in anything but 38/357 44 and 45 colt, so its the over powder/under shot wad, shot, over shot wad, and crimp.
You've always got 2 things working against you: Limited volume in the case for an adequate payload (so bigger cartridges are better). And barrel rifling spins the shot out like a centrifuge, opening patterns. I suspect this is why various companies offered smoothbore 'rifles' around the turn of the century, in cartridges like 44 (as made by Savage, stevens and others IIRC). Many were labelled and marketed as "garden guns" for popping those bunnies.