The pastor, an office clearly inferior to Jesus himself, should bear in min Matt 18:15. In it, Jesus says that for any brother, you should go to him privately, then take witnesses, and only then confront ther person publically. Only aftr all of this, would discipline require being expelled from the church Common sense in regards to pastoral care says this should be a minimum esclatation procedure.
If, in the mind of the pastor this sin is grievous enough to warrant the full discipline of the church, then at the end (and only the end) of this procedure it may require exposing the sin to the church before expelling him.
But keep in mind, while that may be a result, it is most clearly a failure for the pastor I'd he has to get to that point.
what if the person whose sin must be exposed is the pastor?
The target of the accusations and the congregation should remember that donatism is a heresy, and has been thought of as such since the 4th Century. What donatism says is that the efficacy of the sacraments is dependent of the holiness of the minister. That has been explicitly rejected by the church since the time of Augustine for the reasons Augustine wrote.
Thus, even a sinful pastor has a place in the church, as Baaker, Swaggert, et al show.
As Paul says in Philippians 1:18, it doesn't matter whether Christ is preached out of pure motives or impure ones, only that Christ is preached.
What the blackmailer threatens then is not the target's legitimacy before God but rather the efficacy of the leader before man. In attacking a successful church, he is doing a bad thing.
If, however, the target is himself harming the church for other reasons - teaching false doctrine, preying on the innocent, whatever, then it in exposing the sin, he is merely correcting a brother. The bible already has clear procedures in place (confront him privately, bring a brother, then expel him). If exposing the sin is done after these things, then it is just a part of that last step- expelling him from the congregation.