Damascus (twist) barrel shotguns CAN be safe to shoot but GREAT CARE must be taken BEFORE ATTEMPTING TO SHOOT IT! Take it to a gunsmith familiar with old shotguns and let him examine the proofmarks. Based on what he tells you it MAY be shootable. Or it could kill you.
If the gun has been maintained and not allowed to oxidize, it may be shootable. Damascus barrels came with blackpowder, reduced nitro and full nitro proofmarks. Most of these proofs were done LONG AGO and you need the advice of a competent gunsmith.
Then there is the matter of which gauge and what length cartridge the gun is chambered for. As an example, 12 gauge loadings came in 2 inch, 2 1/4, 2 3/8, 2 1/2 as well as 2 3/4 inch shells. THere are also some strange gauges like fourteen gauge in old Damascus guns.
Old shotguns can be great fun to shoot. Damascus is inherently less strong than fluid steel barrels but I have several friends who shoot either nitro-proofed or recent blackpowder-proofed shotguns that have damascus barrels. I personally have a 1886 Boss & Co. but it has fluid steel barrels and was re-proofed at Boss & Co. in London in 1967.
Get it checked out.