HPV is linked to skin cancer, in fact the link was originally found in the 70's if my memory serves me right.

Here's a link

One of the common factors of HPV cancers is a depressed immune system so developing skin cancer after Oral Cancer would make sense considering what the body goes through during treatment and the emotional toll that the experience takes. Anytime stress is involved count on the immune system to tank due to hormone response.

Hope that helps

Eric