All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Scholars are not agreed over the ruling regarding the saliva and hair of dogs. The prevailing opinion is that its saliva is impure based upon evidence that the Prophet ordered washing of recipients which were licked or lapped by a dog. Since there is no evidence establishing the impurity of the fur or hair of the dog, then it is considered pure.
So, if some saliva of the dog touches you, you should remove it, as it is impure. But the scholars have two different opinions regarding how to remove this impurity. Some believe that it should be washed seven times, the same as in the case of licking someone. Other scholars believe that it could be washed as any other impurity; i.e., till removed completely (once, twice, …..).
So, you have the choice to do one or the other.
On the other hand, touching the fur of the dog, whether it is wet or dry, does not require you to wash as the fur of the dog is pure.
Allah knows best.