The 45-rpm record of “Never Smile at a Crocodile,” as sung by Jerry Lewis, was released by Capitol Records in 1953. “Following the Leader” was on the flip side. While “Never Smile at a Crocodile” was written for Peter Pan, it is not sung in the film—there are only portions of the tune used in the background score. After the film was released, the song was recorded by several different singers, including the Paulette Singers and Sterling Holloway. It was also released on sheet music.
[Disney Trivia from the Vault by Dave Smith]