Wikipedia says THEY ALL LAUGHED was introduced in the 1937 film “Shall We Dance?” You can see that scene on YouTube here. In the film, Ginger Rogers sings the entire song, and then she dances to the same tune with Fred Astaire, but Astaire never sings.

But that same year, Fred Astaire recorded the song with Johnny Green and His Orchestra, but Ginger Rogers doesn’t appear on the record. You can hear his recording at the Internet Archive here or here. (Those are two different Brunswick records with different catalog numbers but they were made from the same matrix.)

The Internet Archive also has 1937 recordings by Nat Brandwynne, Jimmy Dorsey, Tommy Dorsey, Nat Harris, Ozzie Nelson, and Red Nichols; and later recordings by George Shearing (1951) and Carmen Mcrae (1955).

The lyrics posted above correspond pretty closely to the way Rogers sings them in the film (except some words are unnecessarily repeated, and there is a coda she doesn’t sing) but Astaire sings them in a different order.