The Colt SAA has been chambered in a myriad of cartridges over its existence, one of them indeed being the 44 Henry RF. It is a desirable collectible due to its rarity.
There was no widely used rifle-pistol cartridge until the 44 WCF was chambered in the SAA. The date of that occurrence used to be set at 1878 but Mike Venturino has reported instances of factory chamberings dating back at least to 1876, IIRC.
1882 specimen.
I don't know the numbers offhand, but there may have been more Smith and Wesson single actions, such as the above, chambered in the 44 RF than there were Colt SAA's. Both are rare guns though.
The first factory conversions were of the Remington Army .44 to a .46 caliber rimfire round...again, IIRC. The Rogers and Spencer is interesting. I'd be very careful what cartridge I shot in it. Word-of-mouth anecdotes about chamberings of such old guns can vary in their accuracy.
Colt Pocket Conversion to 38 Colt.
Conventional wisdom used to be that small charges of smokeless, usually fast-burning powders, were safe in such old guns. I personally would not shoot anything but Black in such a one. Loading black in cartridges is not difficult, but requires some different techniques than smokeless loadings. Any questions would be fielded on the Black Powder Cartridge Rifles forum.
Of course your 44 Colt Uberti is perfectly safe with smokeless, but one mustn't fire anything even approaching hot loads in an open topped design, even one manufactured with modern steels. Frame-stretching can occur very quickly.