Hell has no fury like a woman scorned. I appreciate how unsettling this is to you so take some time to sit and reflect on what course of action might produce the most desireable result. I don't agree with her assessment that what she is trying to do isn't a legal wrong. I believe it is legally wrong.
First of all what would be the purpose of her doing this other than to cause you embarrassment, financial harm, social disgrace, wreck your marriage, etc? None that I can see. Just threatening to do so may be a crime. If she is attempting to obtain anything of value from you the crime may be one of extortion. Civilly it might be consider a tort in that it subjects you to serious and extreme emotional harm.
From a civil standpoint you can handle this one of two ways:
1. Have a private conversation yourself.
2. Hire an attorney who can handle it privately and delicately.
If she does it then you will need to hire a lawyer to sue her for monetary damages. A court might consider enjoining her actions but that would require a public hearing. Hope this helps to guide your actions. Whatever you do don't lose your head and do something stupid. She's obviously not worth your time and energy and you aren't happy with your marriage or you wouldn't be having an affair.