I have a little half stocked percussion rifle that I refer to as a "rook" rifle. It was originally .38 cal, but the bore was fubar, so I sleeved it with a brand new .36 cal Green Mt. barrel. It's a great shooter.
Is yours full stocked? If you make a 20 bore fowling piece out of it, you'll have a barrel that is .065" wall at the muzzle, if it is full stocked. And that's fine.