I would say try a length of hose attached to the hinge, a diameter close to the size of your wiring bundle needed for all the electrical you need in the door. if you tape that to the hinge and it doesn't get hung up then you could use a thin wall tube or hose and put your wires inside it so they are hidden. you may be able to find a ribbon wire as well. like a trailer wiring ribbon wire that has 5 or 6 wires in it. that would keep the bundle low profile in the hinge area and up tight to the metal of the hinge part. you could also look at under carpet wiring suppiers as they have all sorts of ribbon style wiring and covers. this is a link to something that could be used to cover the loose wires in the hinge area. just a thought.
https://www.amazon.ca/UT-Wire-UTW-CP...62803530&psc=1