A very likely possibility that came to mind is that the patch could be BETFOR (British Element Trieste Force), as 1st Scots Gds were part of this from May 1945 until May 1946. The patch in this scenario would have been:
Being a part of the garrison in Trieste would explain the rather dressy nature of the patching, and the reason for using KD regularly in the first place. It doesn't explain the parachutists badge directly but, of course, officers from LRDG units were returned to their parent regiments in 1945, so it could even fit in with that theory too.
Anyway, BETFOR is the best theory i have