Just MHO, but I have seen too many Damascus barrel shot guns that were dangerous to fire with even black powder. I sectioned some and the inside looked like orange lace even though the outside looked good and the bores appeared shiny and rust free. Rifles are usually OK because the barrels are thicker, but even they are subject to the same internal corrosion and rusting as shotgun barrels. The cause is the black powder and corrosive primer residue forced into the crevices of those welded barrels by the pressure. No cleaning can remove it and it continues to do its dirty work unseen while the usual coating of oil keeps the surface area looking shiny.
The better barrels, made by top English makers, are better made and seem less subject to internal corrosion, probably because the welding was done better, with fewer crevices and cracks. Still, those barrels are found on fine old guns, so my advice against firing and taking a chance is based not only on not wanting anyone to be injured, but also on not wanting to see fine old guns destroyed.
Note that this is aside from the question of shooting smokeless powder and modern shells in those guns, something that should never be done, though I have been lectured by folks who do so, including some who claim that they do so all the time, and that Damascus barrels are much stronger than modern steel.