To the contrary, Ricketts always use a Cattleman instead. Very apparent in the ”Easy there, Germany, calm yourself down” mission that I forgot the name of.

That depends on the game itself, because for me he always has either a High Power Pistol or a Schofield Revolver.

Given his comments on the Schofield Revolver and since it's also what he gives us in the first mission we meet him, I think it's safe to assume it was intended to be his preferred weapon.

Sort of reminds me of how Andrew Milton can be seen with a Cattleman Revolver during a cutscene as opposed to his usual Schofield. Keeping in mind the Cattleman is essentially the default weapon of NPCs, in both games mind you, it strikes me as a developer oversight.