Especially during this time period, it would likely mean multiple things before genitalia.

“Dick” was a pretty common word for a detective, as in “hiring a private dick.” These comics are probably chock full of humorous uses of “dick.”

For this one specifically, the first place tineye sees it on the internet is on a “forgotten cool” tumblr in 2015, which also doesn’t cite where it came from.

I was thinking Dick Tracy.