My Stepfather left me a double barrel shotgun with Damascus barrels! doesn't that indicate Black Powder only?
Yes. and, no.
Yes, because of the Damascus construction, and no, because of the age of the gun.
Damascus barrels were made by winding 6 or 8 straps of steel around a mandrel and hammer welding them together. they were considered the top grade available. Cheaper versions used 2 or 4 straps and were called "twist" or "stub twist" barrels.
Made up through the 20s, by some makers before being replaced in the market by solid barrels. Solid "bored" barrels were called "fluid steel" by Ithaca and "Nickel Steel" by Winchester, and I believe other makers had their own trade names.
The problem with Damascus & twist barrels today is from their method of manufacture. Fully safe for black powder when new, now a century of more later there is a risk. The risk is from the hammer welding process, it leaves "gaps" inside the weld, which cannot be seen by visual inspection. And, I don't know of any x-ray or any thing like that that can see inside the gape and tell if there is rust in there, or not.
And that's the risk. Rust, inside the welds weakening them, POSSIBLY to the point where the barrels are no longer safe even for black powder. AND, even if the gun survives being re-proofed that is no guarantee that it won't fail later on.
SO I would recommend all of the old Damascus barrel guns be retired to wall hanger status, just to be on the safe side.
Damascus guns won't "explode" fired with smokeless, in any predicable "time frame" (number of shots). They might go another 100 years or they might let go the next time you pull the trigger, and no one can say when.
Here's a story to illustrate the point,
My Grandfather had an Ithaca gun he liked, and it had twist barrels. A farmer neighbor tried to talk him out of it, and after many years of saying no, he finally gave in and sold the neighbor that gun. He replaced it with another Ithaca, one with fluid steel barrels in 1909. (note the date). I have that gun today, and its still a great gun. The twist barrel gun he sold to his neighbor had 8 inches of the left barrel "unravel" in the early 1940s. The old twist gun lasted another 30+ years and then let go.
I don't have any evidence but it was very likely due to shooting smokeless shells. The fluid steel barrels of my grandfather's gun were rated for smokeless loads when they were made, and are still very good, though not for magnum ammo.
IF otherwise in good shape, you can shoot that Damascus gun with black powder shells. There is a risk, but you can do it, taking suitable precautions. I would not shoot "black powder pressure smokeless loads". While the peak pressure is within black powder limits, the pressure curve of smokeless is different, and could be different enough to cause a Damascus barrel to fail. You just can't tell, until it does fail.
I think the best choice is to retire the Damascus barrel gun. Clean it up (they are pretty) and display it as a relic of days long past.
Certainly better than perhaps losing a finger, or three...