I don't know if my comment earlier was grasped - make your sheath. Slide a piece of cardboard over the teeth and then slide that into the sheath.
The idea that such a thing won't work (especially given that the cardboard could be replaced easily any time) isn't realistic. teeth cut the leather sliding around. Teeth with a cardboard sheath (think the length of the teeth and only one or two inches long) stick into the cardboard, but in hard card won't go through - especially with handling softened by the leather). The sheath slides into the leather. Done.
I got a knife set last week because I wanted the block, and then sold the knives off. Each of them had a simple single cardboard layer sheath and the whole group was in a flat box - no other guard. The knives were shipped sharp, even though they were relatively cheap - a tiny little polished edge all the way along to wow a new customer.
None of the cardboard was damaged by any of the knives, even though they could move around in the box a bit and had no significant protection.
I sold the knives on ebay, same small box in another box, same sheaths - buyer said they all arrived in great shape.
You can make this difficult if you want, but I wouldn't use leather for a saw. If I was going to use leather for a saw, I would put a card sheath on the teeth so that the saw could slide around in the leather without cutting it or the stitches.
(as far as rust goes, line the sheath with anti rust paper if it's a concern - some leathers and other older plastics can do bad things in combination with high humidity (celluloid rot comes to mind - not sure about the various types of tanned leather - but at the very least, it can accidentally get wet, dry and trap some moisture against a blade for a few days out of sight and you'll h pitting then that never goes away).