For the average stuck ball, and I don't see why it wouldn't work on a bullet if one's technique was modified just slightly, Dave Crissalli's, 10-in-1tool, which is aimed at the flintlock shooter, really makes a lot of sense.
There's no reason it can't be used with percussion rifles, you just have an extra tool in the flint knapping hammer.
The tool is called The Gunner's Mate. The company is The Lucky Bag.
THE LUCKY BAG
While some might consider it too expensive, at $88.00, I happen to think it is a bargain (used to be $65.00, but cost of brass went up). Handmade out of solid brass and blued steel.
The tool really comes into its own by CENTERING the drill bit for pilot drilling a hole in a stuck/dry balled patched ball, and keeping the the screw CENTERED in the bore so that it does not wander while screwing itself into the ball. And, furthermore, keeping the entire assembly CENTERED in the bore so as to try and prevent the screw from stripping itself out of the stuck ball.
This is where almost every homemade jury rig tool fails. The hole ends up being drilled off center in the ball, often marring the land & grooves in the process. When that happens, the screw cannot help but go into the ball off center, which ALMOST ALWAYS results in the screw stripping itself out of the ball. Then, the shooter tries to engage the screw into another part of the ball, which results in damaging the bore by gouging it with what most often is a sheet metal screw.
I think every sidelock muzzleloading shooter should have one of these in their pouch.