Several things will determine what you may do in thinning a stock. How is the grain/pore structure aligned? How big is the stock bolt hole? How long is the stock bolt? What kind of wood was used in the stock?
Jim's comment about the size of the reciever is important. It is not so much recoil you have to worry about....it is the stock flex under recoil. Browning is having problems with the Ultra Lite and XS breaking under recoil flex at the back of the receiver due to lack of sufficient (IMO) mass of wood. I have had to repair six so far in the last four months due to this problem. Wood was not too squirrely in structure so can only conclude it had to do with flex of recoil upward causing the breakage.
I would be hesitant to suggest farther than 1/8" OD downsize unless I could really inspect the piece of wood first. Blindness really get one into a boiling kettle sometimes. Can we see pics?
