How about tackling this problem from a different angle? Why not obviate the need for having to hang the coat? I have a couple of ideas:
1) Have all pax leave their jacket outside security at their departing airport at a coatcheck. Then include a jacket as part of C and F amenities
2) Have all pax leave their jacket outside security at their departing airport at a "traveler's jacket" kiosk. When they land at destination they go outside security at arriving airport and select a jacket from those available
I think people actually used to do (and maybe still do) 2 with cigarette lighters