Joe Penner himself appears on this sheet music for DON'T NEVER DO THAT, also known as YOU NASTY MAN. Those were two of his catchphrases, along with "Wanna buy a duck?"
Here is the sheet music inside, which lists Joe Penner among the authors.
Here we have a copy with the title NASTY MAN with a picture of Alice Fay on it. She sang the song in this movie.
At this point they were trying to make Alice Faye look like Jean Harlow, which is why her eyebrows have that look.