Colt started stamping their revolvers with the VP proof on the left forward side edge of the trigger guard in 1904 I believe. That VP proof was their smokeless powder proof.
They advertised that the SAA was suitable for smokeless starting in about 1897,,thats also when they changed the cylinder pin lock from the simple screw to the spring loaded plunger. The cylinder pin lock is often regarded as the best way to tell at a glance if the Colt in hand is a BP or a smokless frame gun.
I believe the 1877 had that springloaded cylinder pin earlier than 1897 if not thru it's entire production.
The 1877 was made till 1909,,so late production should be VP proof stamped if actually proofed for smokeless.
Wether they did that I don't know.
If they did,,did Colt also change the frame, cyl, bbl matl as they did in the SAA back further iin 1897 to take smokeless also,,again I don't know.

I've had a couple of them in 38Colt and I shot very lightly energized 38Spcl W/C handloads from mine.
The bored through early 38Colt chamber allowed them to fit the short cylinder,,I wouldn't shoot factory W/C's in one though.
Any smokeless ammo for an 1877 should be down in the absolute lowest starting range IMO both in deference to the age of the Colts and the borderline yes/no of early smokeless proofing.
Even if smokeless proofed back then,,I don't feel it can be equated to current standards.
Go easy on them,,they are less robust to say the least than a SAA or the later DA Colts.
There's a couple multi-legged springs inside of near miniature proportions asked to do a lot of things and the SA/DA set up is unlike any other I can think of. They have to be just right.