Mizme, the question is,
.. which part is/was broken,
.. the end off the key (winder) or the threaded end of the winding shaft of the mechanism?
My guess is, the end off the key (winder base) was broken off flush with the base of the Santa Claus. And my reasons for said guess is,
..
1. the base of the Santa Claus itself is probably Ό to ½ thick with a hole in the center and the mechanism affixed to the top of it.
2. the threaded end of the winding shaft of the mechanism would not have extended through the base it is affixed too
for reasons of the manufacturing process.
Thus, my 2nd guess is, the broken shaft in the hole of the base
should un-screw from the mechanism
.. and then a new winder with the same thread size made to replace it.
the force required to break off the winding shaft of the mechanism would surely have screwed up the mechanism.