I, too, recognized the song from the movie "I Walked With a Zombie".

Wikipedia has this about Sir Lancelot, who co-starred in at least two Val Lewton films:
"Lancelot Victor Edward Pinard (24 March 1902 – 12 March 2001) was a calypso singer and actor who used the name Sir Lancelot. Sir Lancelot played a major role in popularizing calypso in north America, and Harry Belafonte has acknowledged him as an inspiration and major influence.

Pinard was born in Cumuto, Trinidad, to a fairly affluent family, and thus had a very different background to that of most authentic Trinidadian calypsonians. He sang from an early age, but it was not until he went to New York in 1939 in order to study medicine that he sang calypso, on an invitation of band leader Gerald Clark, who had been impressed by his singing of classical works.

Sir Lancelot toured the west coast with Lionel Belasco's band in 1941, thereby gaining the attention of people in the movie business. His movies include:

I Walked with a Zombie (1943), as a servant who is also a calypso singer. His song "Scandal in the Family" is what reveals the scandal to Betsy, the heroine.
To Have and Have Not (1944), as a (non-singing) assistant to Harry Morgan (Humphrey Bogart).
Happy Go Lucky (1943). Sir Lancelot sings "Ugly Woman", a popular calypso by the Roaring Lion that has been covered by many others (including Robert Mitchum).
Brute Force (1947). Sir Lancelot plays a character named Calypso.
In 1947, Sir Lancelot worked for the presidential campaign of Henry Wallace.

Sir Lancelot's last film appearance was in 1958 (with Buccaneer), but he continued to work as a musician until at least 1973, briefly coming out of retirement in the 1980s to perform at McCabe's Guitar Shop (Los Angeles) with Van Dyke Parks, Ry Cooder and other musicians.

Sir Lancelot died of natural causes in Anaheim, California."

I have mislaid my book about the films of Val Lewton, in which it goes into some detail about the song. If I recall, it was composed by Sir Lancelot, who performs snippets throughout the film.

Here's a link to more info about his filmwork:
Sir Lancelot filmography & music
It notes that he sings a parody of the Holland song in "Zombies on Broadway"!

I haven't a clue about MP3s, but this is a link to downloads, including "Scandal in the Family", as it's listed:
Sir Lancelot ~~MP3 downloads