tempting to pay the £200 isn't it .... but that way lies all sorts of gremlins like A) will he 'go away' B) you are still required to tell your insurance company about the accident.
So, my advice is to put it through as a third party claim, as you say you will not be claiming yourself, yes it will affect your renewal premium but thats life, you will be legal and above board with your insurance company, which, in my view is important.
you may lose some NCD credit, unless you have it covered.