Welcome to the forum, Mr. Scratch.
Just a pity your barrel is not an ancient genuine one ... even probably a recent output
.
If i well understand, it is your desire to give it a nice look, mounting it in a stock format that pleases you and your medieval weapon aficionado friends, althoug not necessarily being an historically matching one.
Don't your friends give you some suggestions themselves? That would increase the probabilities of having a setup that would please them and also please you, at having had their knowledged participation.
On the other hand and as Michael confirms, stock shapes in the old days were a bit "free style" ... pass the term; this not meaning that Chinese mounted their cannons with European stocks and vice versa.
If you search well all (or almost all) the threads in this forum, you will find a countless number of handcannons, with distinct stock attitudes; some original, some following as much as possible the original idea and even some improvisations, result of observing so many examples posted here and also out there.
Then you may certainly be able to improvise your set up, compatible with your and your friends tastes; and also fitting your fireplace mantel.
Meanwhile and concerning freestyle setups, here are some solutions i found for some of my early European barrels.
Also you will find plenty coherent examples if you browse, for example, on Michael (Matchlock) threads.
All the best.
Fernando