I heard he Was A TOBS customer, but dont have much info about that.
I always thought he just sanded his beard off with 100 grit sandpaper.
http://badgerandblade.com/vb/showthread.php/247046-What-John-Wayne-Shaved-With might help. One of the tubes in the picture might be a shaving cream, but there is no brush visible.
He just dry shaved with a bayonet.
he used a cactus juice, kerosene and 80proof whiskey superlather