The point of my original post is the short but especially narrow runway which has very large drops on three sides. Is it a feasible operation
Quite a few runways in the world have large drops at the side or ends! Not ideal but I cannot imagine that this would limit operations if the State had passed the airport as operational. Individual operators might impose a lower crosswind limit due to the width and other factors.
In short (sorry about the pun) so long as you obey the performance regulations and know what you are doing I cannot see any major problem. It would probably be a Cat C or even D airport and operators would have to be satisfied that their pilots are suitably checked out as happens at other airports.
Apparently it's a beautiful unspoilt island - lets hope it doesnt get invaded by too many tourists!