I'm writing as someone who has used and continues to use damascus-barrelled guns for several decades and has spent even more time researching their manufacture, from hand-forged to machine-made, and from coarse tubes to finished gun barrels.
There is no single type of 'damascus'. Any reference to damascus, twist or laminated barrels, each quite different, describes wholly different materials and properties depending on the year and country. Within each type, there is a vast difference in quality, depending on the ratios of steel and iron used, the sources of the steel and iron, and the degree of twisting of these in manufacture. In addition, hand-forged barrels will be quite different from machine-forged barrels. Not knowing what you're dealing with makes the whole exercise one of just guessing, perhaps at the cost of an eye or fingers, and perhaps not your own.
Add to this 100+ years of either good, careful maintenance or neglectful abuse, and you have a great deal of variability. Damascus barrels can rust between the twisted bands, which may not be easily apparent, weakening them significantly. Rust may also develop under the ribs, again away from any visual inspection. Knowing if the barrels are in proof is a good start, and knowing barrel wall thickness is likely to be part of this, as honed or overly-polished barrels bring entirely new risks. Depending on the age of your gun, the chamber length and forcing cone shape may not approach modern dimensions. If your gun is proofed for black powder only, the chamber length (in mm) might not be given in the proof marks.
With old shotguns, pressure is of utmost consideration. This acts on the barrels of course, but also on the action bar and face, fore-end loop, and the stock. Anything which increases pressure unnecessarily has to be given serious thought; subjecting a gun to pressures higher than what it was built for 100+ years ago is foolhardy, and to do so after 100+ years of unknown use, abuse and possible modifications is several degrees worse.
If you are dealing with a gun that was built by the best craftsmen with the best materials, and properly stored, maintained and cared for, time is of lesser concern, and its use might be warranted for several generations of shooters. If you are dealing with a Belgian hardware-store gun, built with the cheapest materials and to the lowest manufacturing standards, then one cannot expect such a gun to last more than a few seasons in the field, if that. Such guns are also far more likely to be 'rode hard and put away wet,' at least for part of their long life. Just because it didn't blow up last time, is no guarantee it won't at the next trigger pull.
There is a lot of expertise on CGN, from many who have been on a lifetime learning curve. Asking people to take the time to provide you with detailed advice and the benefit of their experience, for free, is already much to ask for. Dismiss and diss such advice at your own peril.