As the OP in nostalgia, thank you for posting here. I think that definitively answers the question.
As far as I know, there are no similar flying units these days,(the Falkland Islands Government Air Service is basically an airline, with a small MP role). but there are several ground defence units ( e.g. Royal Bermuda Regiment, Turks & Cacos Regiment, Cayman Regiment, Falklands Defence Force), none of them have an air component.