"The Creeper" sounds just about a perfect fit, judging by what you described.
The only other one I remember having similar plotlines is "The Ape Man" (1943) with Bela Lugosi, and I am not sure if thats the one you are looking for.
http://www.imdb.com/title/tt0035640/
You sure its not Dr Jekyll and Mr Hyde of the 40s?