Try www.tandyleather.com. This is a leather goods company that has
been in business for decades, and although they cater mostly to folks
doing Western-style tooling and saddlery, you can get just about any
leather item there. I don’t know about deer suede (not a commonly
available leather), but they do have deerskin (with the grain on) and
goat or calf leather lacing, both of which will be thin and supple.
The deerskin also has the advantage of incredible stretchiness and
tensile strength. The thick fuzzy stiff stuff is probably split
cowhide, not helpful in jewelry applications.
I’ve also seen pig-suede leather lacing in the past, which is
extremely thin, but still quite strong, and has an interesting grain.
Hope this helps!