Your rifle is a beauty! You are lucky to have it.
Bore diameter means different things to different shooters. People who shoot firearms using fixed ammunition... Breech loaders... Measure bore diameter from the bottom of a groove to the bottom of the opposite groove, or "groove diameter." Muzzleloading shooters think of bore diameter as land to land. The easiest way to remember this is to consider the .44 caliber cap and ball revolvers, which are typically .440" land to land, with grooves .006" to .007" deep, yielding a groove diameter of .452" to .454". So, if you swap your percussion cylinder for a cartridge conversion cylinder, your .44 caliber cap and ball revolver becomes a .45 caliber cartridge revolver, with no modification of the barrel.
What you have there is a .48 caliber (.481") muzzle-loading rifle with grooves slightly over .016" deep, which is pretty deep. Round balls meant to be shot with patches are typically more or less under bore (land to land) size. Most people nowadays start with a ball about .010" under bore size, but old-timers often shot slightly smaller balls than most people use now. Nineteenth century military rifles meant to be shot with patched round balls (e.g. the various Common Rifles, and the M1841 Mississippi Rifle) used balls .015" under bore size for the standard service load. With the grooves as deep as they are in the rifle you have, you'll likely need a pretty thick patch to fill them. Track of the Wolf has .465" round balls in stock, and if it were me, I would start with those and a .020" to .022" patch. In addition, if it were me, I would have a few .457" balls on hand, just in case the .465" balls are hard to load. Those .457" balls are a standard size, and easy to find.
There are certainly people who can custom-make a round ball mould for you in any reasonable size, but I would try some of the ready-made balls to see how they shoot before investing in a mould.
Good luck with it! By all means, let us know how it goes.
Best regards,
Notchy Bob