Well… it ain't Bahamian and it's at least a few years older than we know. That much we're (sort of) sure of at least. Rumor there was the song had Puerto Rican carnival roots, dunno. Good luck with the American pseudonym spaghetti:

Writer's credit on the 1958 Lord Flea Capitol releases was to one “Steve Samuel.” (aka: Gabriel Oller of Spanish Music Company, NY)(Note: Two (2) shakes for the senora.) Shake, Shake, Shake, Senora; w&m Steve Samuel © Spanish Music Center 10Mar50 EU196775 (note: three (3) shakes.)

Oller's NYC record label (SMC Pro-Arte ) was co-founded with WEVD-AM radio DJ Art "Pancho" Raymond and bought out by Oller in 1948. WEVD-AM was also the Moe Asch - Folkways home office.

Credit on the Woody Herman releases was to “Jessie Cavanaugh” (aka: Howie Richmond) of TSO publishers who bought out Moe Asch's Folkways Publishing in 1950, (with Pete Seeger and The Weavers (aka: Paul Campbell.))

Richmond formed Mars Records in 1952; co-managed with Woody Herman.