Shoot, maybe I somehow "cross matched" Luke's characters? I'll have to dig out my VHS stash again & check the name for sure, but Luke's definitely a "new" physician in town in 1944's "Andy Hardy's Blonde Trouble".
Edit: Why didn't I think of this before? IMDB.com has the movie listed, only Luke's character is listed as "Dr. Lee Wong Howe", not "How" like I mistakenly posted. Here's the link:
http://www.imdb.com/title/tt0036602/
Shows how dependable my memory is these days.....
Sorry for the mix-up. Still a great Keye Luke "cameo" though.