SNAKE BELT...

Question

I have just purchased a snake belt. When I purchased it, I remembered a clause i had learned a few years back that a snake never has Tum'at Neveilah. I looked it up in my notes, that according to Eruvin YUD-GIMMEL, Rabenu Tam says that from "Kol Holech Al Gachon" (Vayikra 11:42) he learns that a snake is excluded from Tum'at Neveilah. Thus, is it fine according to halacha to wear it? Thank you.