Could you improvise with plasters?
Cut the sticky bit into narrow strips and use this to pull the wound together, then put a big plaster over the top?
Basically I would think you need something to pull the sides of the wound together to stop the bleeding, then something on top to protect it.
I'm surprised that given that it it such a long way to anywhere that you don't keep a well stocked first aid kit ie wound wash, steri strips, gauze, tape, bandages, plasters of varying sizes, scissors, eye wash, tcp etc.
I sliced my arm open last year whilst smashing up our old iron bath. Despite living very close to A&E and to a miu I did it myself. Washed the wound, then steri stripped it, and put a large plaster over the top. It healed fine within a couple of weeks.
Dh ended up at miu as he dropped a plasterboard on his big toe. I took him a couple of days later when it was clear it wasn't healing. They just put some padding on and a bandage (he has a latex allergy). It still kept bleeding a few days later, so he went to the gp, who passed him onto the nurse. She used a silver colloid solution to seal the wound, which stopped the bleeding (eventually), and gave us loads of dressings to use at home as the dressing needed replacing every day for a week. Good job I'm not squeamish