I have amassed a huge collection of 20th Century pop music, so I can authoritively say people have been recording both the “f” word and subtle reference to the activity it stands for since recording began.
The first were early blues records. The previous poster was right: Lucille Bogan is first. I have two versions of "Shave “Em Dry” from 1935. She said it plain as day on the record.
If you don’t like going that far back, let’s consider the rock music when I was a teenager in the sixties. Yes, Jefferson Airplane sang “Up against the wall, Motherfucker.” I remember the album’s liner notes read “Up against the wall, Fred,” (Fred was code for the Establishment), so all us kids knew who Grace Slick and Crew were calling motherfuckers. The Fugs wanted their group name to be the “Fucks,” but Warner Brothers wouldn’t print it.
Jefferson Airplane’s album “Volunteers” (with the song “We Can Be Together” with the word “motherfucker” in it) was released late in '69, after Woodstock. When it comes to waging war on censorship of free speach, my personal hero is the late Frank Zappa. His Verve album, “Mothermania” was released in early 1969, before “Volunteers.” I was still 15 years old when I first heard the word “fuck” on a record. It was in a song called “Mother People” sung by Frank Zappa and the original Mothers of Invention. Here are the lyrics:
Do you think that my pants are too tight?
Do you think that I’m creepy?
Lemme take a minute & tell you my plan
Lemme take a minute & tell who I am
If it doesn’t show
Think you better know
I’m another person
Better look around before you say you don’t care
Shut your fuckin’ mouth about the length of my hair
How would you survive
If you were alive
Shitty little person?
We are the other people
We are the other people
We are the other people
You’re the other people too
Found a way to get to you"
Zappa did get to me. I never forgot.