Can you shoot BP Cartridges in a modern gun?

I have a Sharps Long Range in 45-90 (Pedersoli) and load my own BP cartridges for it. I saw a Winchester 1886 model lever action in 45-90 yesterday and am curious if I can shoot the same cartridges out of it. Obviously the cleaning would need to be done quickly same as any other BP gun. I know you shouldn't shoot smokeless powder loads in a gun designed for BP, but wondering if it works the other way.

I realize the original 1886 model would have been only shooting BP, but this is a modern gun, just using the same design.