Wiltshire Constabulary were formed in 1839.
Whatever records exist will be held at the Wiltshire and Swindon Family History Centre in Chippenham.
Email is
archives@wiltshire.gov.ukThey are very helpful and will answer enquiries without charge if straightforward, or otherwise will do sone research for you at a reasonable cost.
I agree that it is extremely unlikely that a police officer would have escorted prisoners on a convict ship.
I had a relative who joined the Metropolitan police in the mid 19th C., and the Met certainly have records for individual officers, so I imagine Wiltshire will be the same.