If you want to treat this gun as an investment, do not cut it.
If you don't care what it is worth at the end of the day, and simply want a recreation of another gun, only you know if it's worth it to you - but don't ever expect the recreation to be as valued by others as your unaltered shotgun would have been.
Personally, I'm of two minds. I hate seeing quality old guns destroyed for any reason, BUT, if the trench gun you are speaking of is so rare as to make it virtually unobtainable, and a person is trying to recreate a seldom seen weapon for historical purposes, then the sacrifice of a more common gun does serve a purpose.
If you just like short shotguns, I'd say either keep what you have and buy another for that purpose, or sell this one and use it to fund the other project. If the purpose is the beginning of an honest attempt at recreating the other gun, I would not hold the destruction of the Win97 against you.