Treat the cape like meat, it will be fine. I've kept unsalted hides up to a week in the field, but it wasn't super hot. I was sweating it on one trip with two capes and it being 60-65 deg for 2 days. They turned out ok though. I skin the head, split it, and get all the meat off . It doesn't hurt it to let it dry out. Less moisture is less chance of spoilage. Keep it shaded and cool, and in a game bag to keep the flies off. I've yet to salt a sheep cape in the field out of about a dozen, and never had an issue. Taking a couple pounds of salt wouldn't hurt to leave at the strip just in case, if you were to fly in. I have salted moose capes, but had room to fly in 15lbs of salt. It saved about that much in weight going home, but we were loaded too.
I always pack out the skull, so no help on a light weight the saw. I am in the hunt for a new one myself.
Not sure how much weight you really save by cutting, I always pack them out. I've weighed most of my skull/horns when I get home with them, they've range from 18-22lbs green. A clean skull no horns is almost exactly 4lbs on a half dozen I've weighed. meat cleaned up no brains/wet they are about 4.5 to maybe 5 tops. I have no idea what the skull cap would weigh, but most of the weight is in the horn cores and top of the skull. I suppose you could save a pound or two but cutting it, so the saw would make sense I suppose. Its a good problem to have!
Good luck on your hunt! I'm counting the days, and hope the smoke clears out.