If one sorts by job title and work practice, as opposed to language or race, there is a direction connection between calypso and Western nautical work song.

Standard model: Calypso music
“Calypso is a style of Afro-Caribbean music that originated in Trinidad and Tobago during the early to the mid-19th century and spread to the rest of the Caribbean Antilles and Venezuela by the mid-20th century. Its rhythms can be traced back to West African Kaiso and the arrival of French planters and their slaves from the French Antilles in the 18th century.

It is characterized by highly rhythmic and harmonic vocals, and is most often sung in a French creole and led by a griot. As calypso developed, the role of the griot became known as a chantuelle and eventually, calypsonian. As English replaced "patois" (Antillean creole) as the dominant language, calypso migrated into English,...”

Calypsonian
“Origin
Calypso music was developed in Trinidad in the 17th century from the West African kaiso and canboulay music brought by African slaves imported to that Caribbean island to work on sugar plantations. They were stripped of all connections to their homeland and family and not allowed to talk to each other. African griots (musicians and storytellers) among the slaves used calypso song to mock the slave-masters and to communicate with each other. As calypso developed, the African griots became later-generation chantuelles or "chantwells" preserving their people's history and traditions orally, a role that would eventually develop into that of the modern calypsonian.”

In contemporary dictionaries griot isn't an 'African' word, tradition or practice. Gritador was a proper “Western” job title. The standard definition of gritaria was: the rhythmic sounds mariners make when going about any task in unison… or words to that effect. The Western practice is pre-historic.

Where that leaves the etymology of the “chantyman” I can't say, but it certainly fits with the alternate job titles for the period under discussion.