The body of a sheretz conveys impurity. The translations of the animals that count as Sheratzim (listed in Parashat Shemini) often include weasels or ferrets as well as rats, insects, and lizards.
Streimels (and fur coats) are often made from furry weasel like animals (martens, ferrets, raccoons, muskrats).
Why don't the wearers of these furs and pelts become impure from handling the bodies of sheratzim? Does it matter if the hat still has the animals' head attached?