Any Mauser bayo should fit that carbine. The lug the bayo slips on were standard, but tolerances sometimes varied enough that 'any bayo' may not go on a certain rifle. The rod/barrel overhang, looks longer then the rifle, so longer handled bayo may be needed.
Many of these carbines were rebuilt and new wood added during rebuild.
PS: just tried my rifle bayo on carbine, it fits with rod removed so the hole must be deeper for the rod in a carbine bayo. My rods (rifle, carbine) seem the same length as yours.