At the start of this campaign the Royal Corps of Military Articifers raised a company of articifers at Spithead, Hampshire, for service in the West Indies under the command of Lt Col. C Shipley. This company was known as the West India Company, and they suffered a high level of casualties due to Yellow Fever. The Corps of Military Articifers were to eventually become part of the Royal Engineers.
The National Archives at Kew, hold documents relating to the payment of this Prize Money, which was made in two installments, so it could be worth checking these to see if your man is there. For the Articifiers the Catalogue Ref. is WO 164/38, and the Royal Engineers WO 164/39. There are different references for the second installment, again prefixed WO 164.
Martin