Howdy
First of all, I would take it to a gunsmith who is familiar with toggle link rifles and have him determine how tight the action is. If the smith blesses it, if the toggles and bolt lock up nice and tight and if the headspace is correct, I would not hesitate to shoot it with light Smokeless loads, such as cowboy loads.
A rifle is not the same as a revolver. While I never shoot pre-1900 revolvers with Smokeless, the barrel thickness at the chamber is plenty heavy enough for light smokeless loads. The only question is, do the toggles and bolt lock up correctly without any slop. If there is excess slop, if the headspace is not correct, than Smokeless loads will pound the dickens out of the links and mortices, and make things worse. But if everything is nice and tight, light loads Smokeless loads won't hurt it.
Of course, if it was mine, I would put nothing but BP through it. So far I have five rifles chambered for 44-40, I only shoot BP in them. I have one original 1873 made in 1887, chambered for 38-40. It only sees Black Powder too.