I had a short flight with 84 Sqdn when I was at Akrotiri for easter camp back in 1986; course they were flying Wessex in those days.(Yes I did see the knickers)
Can't help thinking it might have been easier to stick the Puma(s) in a C17 rather than fly them all the way to Cyprus; that last leg (overwater avoiding Turkish airspace) could be a bit dodgy.
I have a great affection for Pumas; I did a flight out of Farnborough in a Puma with Andy Warner (who later became CTP of Eurocopter) in the right hand seat (I was left hand seat) low level around Salisbury Plain in one below the treetops.