Whistling in the Dark was a 1931 Hit of the Week. These were cardboard records sold via newsstands for 15 cents during the Great Depression.

Hit of the Week records were promoted in 1929 with the following:

“This is the new Hit-of-the-week record. It is made of Durium, the great invention of a Columbia university professor. Its tone is as rich as the costliest record made. It is guaranteed to play perfectly longer than any other record. It won’t break if you drop it. It brings you the latest dance hits each week played by Broadway’s best orchestras, at the sensationally low price of fifteen cents! Each week our music jury, composed of Florenz Ziegfeld, Eddie Cantor and Vincent Lopez, selects the outstanding dance hits of the hour for the Hit-of-the-week recording. A new Hit-of-the-week record is on sale each Thursday at all news-stands in this city. Fifteen cents!” (source)

Digital Sheet Music Download for sale here (unless you are in U.S., Canada or Venezuela).
Shirts, posters, greeting cards and mugs with an image of sheet music for the song available here.

Radio Dismuke – Online station of 1920s & 1930s Popular Music and Jazz

They Might Be Giants’ Whistling in the Dark here