If you read up on the Entertainment Industry at the time, trick shooters and the like used a lot of smoothbore rifles with shot loads for their trick shooting demonstrations.
That's one possible explanation.
Seen it mentioned in several books and articles wrt folks like Annie Oakley, and such.
Lots of off-the-shelf shot loads available for the 44-40.
Spend the money on a letter from the Cody Museum. They may be able to tell you the original configuration as well as when and to whom it was shipped.
Can't help with parts.
Cheers
Trev