I thought both the British West Indies Regiment and the West India Regiment were disbanded between the wars?
The Islands had local volunteer defence forces. They were divided into the North Caribbean Force and the South Caribbean Force. The North force was made up of volunteers from Jamaica, the Leeward Islands, the Bahamas and British Honduras (Belize). The South Force consisted of men from Barbados, British Guiana, the Windward Islands and Trinidad.
A composite force called the Caribbean Regiment was formed from these in 1944, and while it served overseas, I don't think it actually saw any fighting.
Men of the South Caribbean Force in training...
St. Lucia Volunteer Force, Windward Islands (South Carribean Force)...
A more traditional way of training in the West Indies...
Men of the Trinidad Royal Naval Volunteer Reserve.
Off to war...
About to leave for service overseas, Trinidad 1944.
The Islands also had ATS units.
Jamaican ATS
Trinidadian ATS
Lots of West Indians travelled to Britain and joined the British Army (there was nothing stopping them doing this). There were supposedly two black soldiers in Major Howard's command that took Pegasus Bridge on D-Day (though I don't know if they were West Indians or British-born).