How to hide Facebook chat

I had some erotic chats with some persons on Facebook which are not my friends there anymore. If I delete this chats in my account it would be gone from my account but on girls account it would still be. So if someone goes to this girls profile it can see it. If i block this girls people can still see that she chat with me (name and little profile picture would still be seen). If I delete may Facebook profile and make new one the problem would be fixed because before I delete my account I can change my name and nobody would know it was me in chat. But I would like to know if there is some better option? And don't tell me to ask girls to delete chat because we don't have conversations any more.

One more thing. It was not many chats like that (around 5) but anyway i don't like this chats.