There was a weekly radio feature column which ran nothing but jokes from various comedy shows over the course of the week.
This one is dated May 4, 1938. I'll transcribe the part about Jack. You can read the .jpg of the column for all of them.
The Week's Wireless Wisecracks, Etheric Epigrams and Aerial Aphorisms
Jack Benny: What's your husband doing in the kitchen?
Actress: He's got his wooden leg in the stove; we're outa coal.
Jack Benny: Oh, you're outa coal.
Actor: OUCH!
Actress: What's the matter, Lem?
Actor: We're outa wood, too.
Jack Benny: Say, you look pretty spry for a man eighty-two. You stand so straight and erect.
Andy Devine: Shucks, my arteries are so hard I can't bend over.
Jack Benny: Tell me, Kenny, how's your Maw and Paw?
Kenny Baker: Not so good, Buck, they were playing tennis yesterday and Paw got his beard caught in the racket. He's in pretty bad shape.
Jack Benny: Why, what happened?
Kenny Baker: He swung at the ball and broke his neck.
Jack Benny & Co., NBC Red Network
Sundays, 7:00 p.m., EST.