In reality the Black Powder pistols labeled as 44, are in fact 45 caliber and then you add a bit for chamber sealing (ie prevent chain fires though there is disagreement on what the best protection from a chain fire is).
That gets back to the conventions of when those guns were built originally and how we would address calibers today (least we forget a .357/38 special are both the same caliber. A .41 magnum is a true .410 where a 44 magnum is not. My 7.5 Swiss rifles are actually 30 caliber (7.62 as it were). So you go with the reality.
The Cartridge conversion for those guns are 45 colt.
Current reproductions (as best I know) recommend .454 round balls. Having checked the seal (band width) at least mine has a nice .147 wide band. There can be chambers that are not sized right or oval so the shaved lead ring is not a given for a good seal (I go with the seal aspect but that is my take)
The ROA specifies a .457 round ball. I will test that when mine arrives and see what the width of the band is.
The Ameri San Paola (ASP) New Model Army my wife gave me came with .457 balls, it does not shave lead, it has a tapered cahmbers so the .457 goes in easily and then squeezes to a .250 wide band.
I believe its bore is also wider as you shoot a .457 ball in the Pietta NMA I have and the ASP NMA, the Pietta is 100 fps slower.
Put in the recommended .454 and its on par with the ASP velocity wise for the same load.