If you are talking about this vent assembly, you cannot buy a "vane"
The vane may have come adrift, but the two vanes are connected internally by linkage which is probably broken internally. This probably means there are broken parts inside the vent assembly and that even if you did manage to somehow replace the upper vane, they would not open correctly because the linkage is broken.
Your proposed solution of carving one out of wood sounds interesting. Please document with pictures. :lurk: