Nothing to do with the military. Airfields, or at least fields used for landing on most of the Orkney Islands, were established by Edmund Fresson of Highland Airways in 1934. The first landing on Papa Westray was made by him in 1945 when consideration was being given to restarting inter island air services in Orkney post war.
However the dead hand of the nationalised airline put paid to that happening until in 1967 Loganair recommenced inter island services with the then new Islander aircraft. I believe a newly constructed field at Westray replaced the one that had been used pre war by Fresson, as only the North Ronaldsay and Sanday airfields are the same as those used pre war. The Papa Westray strip may be the same field surveyed by him in 1945 as there is a limited choice of fields on that small island.