I think sabots in cap and ball revolvers would be a waste of time.
Let's consider a .44 sabot designed for a .38-caliber (.35-caliber, actually) bullet.
A sabot must, by necessity, take up more space than a regular .44 ball or conical bullet.
Cap and ball revolvers have limited powder capacities. The Walker and Dragoons have the largest chamber volume of the .44 revolvers, the 1860 Colt has the smallest (discounting the inauthentic 1851 Navy in .44-caliber, which never existed back then).
So, with a sabot, you cannot expect to use as much powder as you would with a lead ball.
Rifles don't have this problem. You can add as much powder as you (safely) wish without concern for the total length of your load column.
With revolvers, of course, you are limited to cramming everything at least flush with the face of the chamber, so the cylinder will revolve freely.
Then there's the problem of lubrication.
Most rifle sabots have a lubricating disk attached to their base, or you load the lubricating disk separately, twixt powder and sabot.
So, you'd have to lubricate the sabot somehow, to keep fouling soft. Remember, you're not firing one shot and then swabbing the bore. You're firing six rounds before the bore can be swabbed.
Black powder fouling and plastic from the sabot would undoubtedly build quickly in the bore.
Perhaps grease over the sabot, after it's seated, would work. It works (to a degree) for the lead ball but I suspect the sabot will only push the lubricant ahead of it and not allow the lubricant to soften the fouling.
A sabot with ridges around its circumference, to hold a small amount of lubricant, might work. But these ridges might encourage blow-by as the sabot crosses that critical juncture between chamber mouth and forcing cone (rear of the barrel).
You might find that this blow-by also blows all the lubricant off the sabot.
I suspect a lubricating disk of some type, probably felt, between powder and sabot, would work best.
So, now you're faced with using some kind of lubricating disk twixt powder and sabot, further increasing the length of your load column.
In order to keep the whole works from projecting out of the cylinder, and tying up the whole works by preventing the cylinder from turning, you have to reduce the total length of your load column.
Something has to give, and the only thing you can reduce is powder.
Now that's a real problem.
You originally adopted a sabot to shoot a lighter bullet at a higher speed. Now, you are forced to cut back on the powder charge --- thereby reducing velocity.
Also, there are other considerations.
The sabot may "catch" slightly on the gap between the cylinder and rear of the barrel. This would be terribly detrimental to accuracy. Rifles who shoot sabots don't have this gap with which to contend.
Let's say you do make it work, and get more velocity.
In handguns, old and modern, the faster you propel a bullet the lower it strikes on target.
This might be a problem in cap and ball revolvers without adjustable sights. Only testing would determine HOW low that shot might strike but it may be so low that you can't compensate for it, with either aiming high or using adjustable sights.
This would negate the sabots in a revolver for hunting, since hunting requires very precise bullet placement.
Finally, what's the point?
You bought a replica of an old-time revolver to experience vicariously what the soldiers and gunmen of yore experienced.
The cap and ball revolver shouldn't be the platform for experiments to gain more velocity. They're simply not made for it.
Would you put a 427 hemi engine in a Ford Pinto?
I guess I'm just an old fuddy-duddy but I feel that nothing but lead bullets should be fired in a cap and ball revolver. If you MUST have something more powerful, buy a modern cartridge handgun.
Firing a plastic projectile down the bore of a cap and ball seems, to me, an insult. You'd never find me profaning my revolvers in such a manner.