You could say yes.
I mean, your world has some kind of legislative body, right? Maybe one of your FoNs sits on it. Let’s say that body passes a budget every year, and your FoN wants to amend that budget (this is very much in the idiom of 20th century democratic legislatures, of course, but it could be a privy council or a court of ministers or whatever too). There’s a formal debate over this. Do you hold a Duel of Wits, rolling dice against yourself? I sure hope not! If none of the PCs have a stake in it (either direct or at one remove*), just say yes. Cover it with a color scene or interstitial. You might need a builder to find the target, if you don’t already have a relationship with them.
If that seems uncomfortable to you and you feel that there is a PC with enough stake in the duel that it needs to be rolled for, just run the duel. Hand the NPC over to the appropriate player and go for it. Duels against non-Psychologists don’t last long, usually.
Also, remember that if you Psychologist has the Psychologist’s Code trait, this (almost) automatically earns them the Codebreaker trait. Even if they don’t, it certainly makes them eligible at the next trait vote. That means they get a 1d infamous rep among “colleagues and anyone else who knows them.”
To answer the corollary-questions:
- There is no “I Corner Him And Stab Him In The Brain” equivalent to the Psychic Duel. There is a short-form Firefight, but no short-form Duel (either of Wits or Psychic).
- There is such a thing as a Psychology Versus test. You could, for instance, have two Psychologists both trying to Read the same individual before the other did. However, if you want the effects of a Psychic Duel (changing beliefs or traits) you need to Duel. You can’t just skip over it with one roll (though you can Say Yes to the duel if appropriate).
*By which I mean, if you’re not hitting a PC or one of a PC’s relationships, or a leader of a faction that’s been activated by the PC’s side in the Infection, or in some other way someone that a PC has a mechanical link to, you can just do it. And having a Belief about an NPC isn’t enough by itself to protect them. But if it’s a PC’s relationship or a PC-controlled faction, you probably need to do the whole thing.