I sort of doubt that any legal rights would be extended to vampires as a matter of course were they found out, so I'd side with Alicorn on this one. Turning and indoctrinating your own larger vamp police force on the sly would probably be more productive, but obviously also risky. Use fierce human rights activists? ;]

One could arrange to out vampires if they don't behave (including if the one threatening this is killed) and therefore call the collective wrath of the human military industrial complex upon them (see The Salvation War ;). Of course, this would require that most vamps would see the threat as credible and dangerous, and would co-operate in policing the unavoidable defectors efficiently enough for the blackmailer to be satisfied. This may be a tall order, and could lead to open war on follow-through.