Please provide background from how it started, how you discovered, if wife did not confess how she reacted, and how it was ended. Every detail is important please post in full.
Since you chose an option along with your pastor and wife you need to discuss with them what and how the response should be. I would lean very strongly towards exposure. I would also push for your wife to take the lead in confronting him. Ideally she, your pastor and yourself should confront in person to show a united front. This is the very bet option at this point, let me explain why.
First the purpose of exspouse is to destroy the affair and prevent the adulters from taking the affair underground, preventing friends with good values from weighing in, then seeking surpport from those friends in the future when they bring the relationship public after destroying the chacter of the BS and then divorceing. It should follow the guidelines from marriage builders Exposure 101 - Your Most Powerful Weapon - Marriage Builders® Forums
How experienced is your pastor with dealing with adultery ? What is his training and philosophy: ie does he/she rugsweep? How was the descion made to not expose made? Did you discuss John's parable of the tax collector's reaction to the light? Perhaps not just greed drove him back into the dark, but fear also of standing in the light exposed all to see him.
Tell the pastor and your wife you need to see them without telling why until you meet. When all together in person focus on your wife's reaction when you share the info. You and the pastor need to see her intial reaction and suggestion. Yes this does have an element of a shyt test but is necessary. I stated earlier she needs to take the lead in dealing with posm with yours and the pastor's support. Please read up on heavy lifting, accepting responsibility, and of consequences. She needs to prove to herself and then you that she is a strong, capable adult, who can be trusted to handle adult relationships. If she does succeed it with strengthen her and your marriage.
Please take the time to share the history of their adultery. Without it the advise may cause more harm then good and leave you personal very vulnerable.
Take care and be strong