The three ways I know of to get a dryball out of a caplock are powder under the nipple (or into the cleanout screw if there is one), screw type worm, or CO2 discharger. Any can work, but any can fail as well, depending on conditions. (Actually, there's a fourth way - unbreeching, but it's obviously a last resort.)
CO2 has the advantage that it's probably quickest, which is an advantage if you have to use it in the middle of a match relay where time is a factor. Sometimes (especially on a flinter) you can't get a good enough gas seal to build up sufficient pressure to move the ball.
Powder under the nipple will work, the finer grain the better. If the first try doesn't clear the ball from the barrel, you can repeat the process but remember to seat the ball back atop the powder so you don't have an air gap between powder and ball. And remember that the 'dryball' might actually be a misfire, so keep the barrel pointed in a safe direction at all times in case there's a loud boom when the ball does come out.
Ball puller has the potential of drilling a hole clean through the ball and stripping out when you pull, leaving you a lead donut down there that the puller can no longer screw into and that now can't be removed by CO2 or powder, so I try the other methods first. For the screw puller, I'd recommend using a metal range rod with a brass muzzle protector collar when possible.
All the methods work best if you clean the bore to get most of the fouling out and put a little lube down to slick things up and reduce the work the CO2/powder/worm has to do to get the ball and patch out.