I'd advise just skinning this bird...not worth heating water to pluck one lonely bird, trust me! Plus...that skin has been exposed, is tough and won't do much for your bird's taste at this point.
Let me see if I have any pics I can dig up for you about processing......
One option you might try is to just let this bird be....you can place some bag balm or other heavy ointment like A&D on her and she will do fine this winter. I've seen some pretty badly moulting birds make it through the cold just fine.
A killing cone is very easily constructed out of a bleach jug...they are surprisingly sturdy and you can just tack them to a tree so you have hands free to do the throat slitting. Just cut the top out enough to accommodate a head and neck, cut the bottom out, invert so the bottom hole is topside and tack it up....killing cone that lasts a long time!
When you go to cut the throat, place tension on the skin by pulling gently downward on the beak, like so:
When starting to gut, cut gently and slowly around the vent area...don't puncture the bowels, but if you do, don't panic...it will wash right off the meat and won't cause any permanent taste problems:
After you have cut those ligaments and other attachments loose, just gently pull out the bowel/vent area to keep it away from the bird while you open the cavity and pull out the other organs:
When skinning, you can remove the skin much like you would remove a jacket...first one wing and leg, work the skin loose from the back and then off the other set of extremities. Cutting off the wings at the first joint will make this easier....there isn't any meat there on a layer anyway.
Good luck! Keep us posted?