The Big Clock, made that same year, also features Harry Morgan as a mute character.

He does have a very expressive face. And looks, at least as Billy Scripture, slightly like another actor, I just haven't been able to figure out whom. I had this problem with Anton Walbrook minus his characteristic mustache in The Queen of Spades (1949).

This sounds interesting; will check it out.

It's streaming on Amazon! Does that do you any good?