Here's the ol Roo Skin Sling I made as a teenager many many years ago, still going strong to this day and no doubt will see me out and probably my kids and grand kids too. I can't remember if I bothered tanning it as such, but I do remember breaking the hide on a wire fence which worked a treat and made it nice and supple, I recently gave it a bit of leather dressing to keep it supple too, other than that it's had nothing done to it what so ever.
It's lovely to use, it doesn't dig into you at all and it wraps around the forearm perfectly to aid in getting a steady aim.