Yes, you can back up your database and if you’re rooted, you can find a key to it, but that will give you the chat in database form. You won’t get your pictures and videos etc. You can download them seperately though.
Yes, you can export a single chat / chatgroup, but doing that for the thousands of chats you probably have is not practically possible.
So you’re stuck. Either you share all your data with Facebook or you get rid of your chat history.
Lock down the permissions WhatsApp has – it has way too many!