To be specific, Godfrey uses the standard human male model with the Lich King's skeleton.

For those who aren't aware, WoW (and most modern games and other types of 3D animation)'s characters/NPCs work similar to a real body: the model is the "flesh" of the NPC, while the skeleton is the NPC's skeletal system and dictates the NPC's movements and animations. Early in the WotLK beta, the Lich King model lacked his own skeleton and instead used the standard human male one. Later, the he was given his own skeleton, but the model remained the same.

Basically, this means that both the human male model and the Lich King's model are compatible with and can be animated with each other's skeletons.