I flew in commercial a few years ago.
It is/was a small airport solely given to tourist flights and I saw no evidence of GA.
The landing was a nailbiter: our AC Airbus (IIRC) shuddered to a halt on the end turning circle of the runway overlooking the sea.(the runway goes from one side of a narrow bit of the island to the other and is quite short.)
The flight out comes in with just enough fuel to take off with full pax and fly to the Greek mainland, where it lands to pick up enough fuel to get home.
May have changed now of course.
Try the airlines forum for a contact number.
Cheers
Cusco