Although you may not be thrilled with the frankness of the answer, I believe you need to do two things. First, you need to talk to your wife and explained the situation to her. Explain how you love her, explain how you are happy in your relationship, explain how you are not perfect and that she made a mistake. Then asked for her forgiveness and explain what has happened. Second, you should go to the police and file a complaint.
Although this may seem difficult, the alternative is potentially having your secret exposed not on your terms or you may wind up paying blackmail money with no assurance that the person seeking to blackmail you will not come back later and seek to extract more money from you since they know you are willing to pay off.
The only way for you to be certain that no harm will come to you (or to limit any potential damage to your relationship) would be to take the following steps. Although it may be difficult and ordered this tasteful and most likely very embarrassing to have this discussion with your wife, it truly is the best way to address the issue.