Bailing twine. Tried and true, recommended by hillbillies everywhere.
Seriously, a $400.00 custom leather sling ain't gonna make that gun shoot one bit better.
Twine is inexpensive, it's quiet, it's readily available and it works.
If you want something unique, get grandma to knit you one. I'll guarantee there won't be another like it in any Deer camp in North America.
Is you pride in your weapon or your tool, you decide.