Pieces from the belly are most likely to stretch, and work easily over a wooden core. Tandy's leather craft chain is a convenient source for small quantities. They may cost a little more, but you can buy small quantities, you'll be sure of getting tooling leather. I like to sew with linen thread. It costs a little more than the artificial stuff, but it's traditional, and makes a nice appearance.
Artificial sinew is a cheaper, durable alternative.
If you're being very historically accurate, and doing American colonial period, you may want brain tanned leather, and real sinew. If you have ready access to these materials however, you probably don't need this primer. If you are going to line the sheath with wood, you can use any wood not prone to splitting. Basswood is light in weight and easy to carve. I expect Birch would be the common wood used for the purpose in traditional Scandinavia.