Aw! Poor Cooper.... hope your problem gets resolved quickly.
Peek A Boo had a 'lipstick' problem a while back... upon very close examination (by me, lol), I could see that some of his hair was getting stuck to him, and prevented his pee part from retracting completely. So I lubed him up real good, and was able to get the hairs unstuck, then he got a bit of a trim. He hasn't had a problem since, and it never interfered with his cat-humping activities.
Hoping Coopie feels better soon!
Hugs,