Wikipedia says this:
"Children of the World" was the working title of the attraction. The attraction's tentative soundtrack design featured each national anthem, playing all at once, which resulted in a cacophonous noise. Walt demonstrated the miniature mock-up to his staff songwriters Robert B. Sherman and Richard M. Sherman. As he and the Sherman Brothers walked through Walt said, "I need one song" a single song for the attraction which could be easily translated into many different languages and which could be played in round. The Sherman Brothers wrote "It's a small world (after all)" in the wake of the Cuban Missile Crisis, which influenced the song's message. They first presented "It's a small world (after all)" to Walt by singing in counterpoint while walking through the mock-up. The attraction became known as "it's a small world" after Walt Disney approved the Sherman Brothers' title song.
In the spirit of international unity, "It's a small world (after all)" was sung and recorded in various studios around the world – by a church choir in London, TV performers in Mexico City, a school chorus in Rome, and by local children from Tokyo and California.
It is argued that this song is the single most performed and most widely translated song on earth. The song tune and lyrics are the only Disney creations never to be copyrighted, as UNICEF requested, and can be heard worldwide on musical devices ranging from keyboard demos to ice cream trucks; it remains "a gift to the children of the world."
So no, it's not from a Disney film...
