Chic, Nice gun and very nice to have those added features.
In my opinion, I would try and fix the other stock first. If it was broken in two pieces at the wrist, better yet providing it will come apart. First you have to take wood from receiver, if stock will not come apart, I would work carefully along the break removing excess glue or what ever used. Clean area thoroughly and if there is a glue line that can be fixed with furniture pens of a color very close to what you have or by blending a few different colors in. Refinish stock and touch up checkering if need be and put a nice oil finish back on it.
Unless the other stock is also a Hunter One-Trigger it will not fit. The opening in the stock for the single trigger is larger and had to have more wood removed. I did this to a 16 ga, stock was too short and messed up, replaced it with an Ideal Grade. I used a mortising machine that I use in wood working and a 3/8" mortising chisel. Set old stock near area and copied that stock by removing the excess wood. Nerve racking to say the least, but it worked great.
So in my opinion I would try the old stock first, nothing to loose.
Are the old barrels Damascus, and if they are no good, do you have any plans for them? The reason I ask is that I am experimenting with black/white re-bluing and brown/white rusting and would use segments of these barrels for test pieces.