Follow K80's advice.
Many people are safely shooting damascus shotguns and have been for years.
I personally prefer them, as there will never be another damascus barrel made, at least not by the original methods.
Whatever you do, DO NOT alter the barrels on your Parker. Parkers are collectible, but really only if they are in original condition. Any of the above suggestions will drastically reduce the value of your gun, while costing you a fair amount to do so.
My best suggestion is to read, read, read, and ask alot of questions. I was in the same position as you are a few years ago. I also held alot of the same erroneous opinions as stated above.
I am NOT saying your gun is safe to shoot, that will need judgement and experience that you don't have yet. Send it to a competent SxS gunsmith (NOT the local bolt action guy) for evaluation and opinion.
Load blackpowder if you like, that was the first step I took until I became more familiar with these older guns and in particular damascus guns. If you look there are now lots of specialty ammo manufacturers that load appropriate pressure ammunition.
Remember, your gun may or may not be safe to shoot, but don't start wrecking it before you know what you are doing.
My best suggestion is to follow the advice to post your questions on the BBS at
www.gunshop.com
OK, let the flames begin. I found this post via a google search for something else and have not ever posted here before. I will admit it is unlikely I will return, but the misinformation above demanded another option for this question.
Best,
Mike