I'll admit my Veloviewer max square has not got down as far as Heathrow yet, but I'm not far off (it would be my SE corner) so I have done a tiny bit of research on this. Looking at the map, you would be able to cross off all of the Heathrow squares by using the Perimeter Road(s) (e.g. no need to go into the central area of the airport), although none of them are probably particularly nice to ride on given the amount of traffic.
However OpenCycleMap does seem to suggest that at least half the perimeter does have shared cycle/pedestrian paths running alongside the roads - almost all of the west side, half the south side and some of the east, so that might make things a bit easier to navigate.