One, OP, you can reread your severance agreement to appreciate the likely consequences of your breaching its confidential provisions. I would presume the agreement incorporates a substantial liquidated damages clause and/or other clauses setting forth what your employer could obtain if you breach confidentiality.
Two, why do you want to cause harm to your former lover? Presumably, you were both adults. You both engaged in consensual adult conduct. Nothing in your posts indicates that he harassed you or took advantage of you in any way. You understood that he was married when you commenced the affair. You had to realize that you would likely come out “on the short end of the stick” if and when your affair soured. The fact your married former supervisor now wants to cover up his illicit relationship with you is not surprising.
Your potential efforts to expose him likely are unlawful and will have significant deleterious repercussions for you. Instead of giving into your “ugly side,” you should listen to the parts of you which make you “beautiful.” Respectfully, you should take the high road, own your own mistakes and move on.