Does touching the skin or hair of a predatory animal—such as a dog or a wolf—if the animal is impure, invalidate ablution, and is it impure like the impurity of its saliva?

Every living animal is entirely pure, and so is its leftover (sû’r), except for its urine and droppings, with the exception of the dog and the pig, and whatever is born from them or from one of them. These two are intrinsically impure, whether alive or dead. Touching an impure animal does not invalidate ablution (wudû’), but it does render impure the part that comes into contact with it if both are wet or one of them is wet. This part must then be washed before prayer and the like. However, if both are dry, the part that touches it does not become impure.