If your threat is "my heavies," "my organization, which is known to assassinate people," etc. rather than "me" or "my gun," it's still a threat of violence. Thugs and armies are weapons, just not ones you can wear around your waist like a black belt or carry in your hand like an M1911. All of the above are Intimidation.
Whereas if your threat is actually "your career is sunk" or "my organization, which is also yours and I'm your boss," it's no longer a threat of violence. Depending on how it's done, that might be Administration, Law, Leadership, Politics, Savoir-Faire, or Streetwise.
The litmus for
all social skills is "What tool am I using?", not "What emotion am I playing on?" or "What result do I want?" Influence skills involve tool use, it's just that the tools aren't usually physical:
- Diplomacy uses the tool of bargaining: "Do what I say because here are lists of what we each have to offer and lose, and you have less to offer or more to lose."
- Intimidation uses the tool of violence: "Do what I say, or your or your loved ones get hurt."
- Fast-Talk uses the tool of deception: "Do what I say because I said it glibly enough for nonsense to make sense."
- Savoir-Faire uses the tool of legitimate authority: "Do what I say because I'm super-important in polite society."
- Sex Appeal uses the tool of sex: "Do what I say because I'm just that hot."
- Streetwise uses the tool of criminal connections: "Do what I say because I'm super-important in low society."
The same goes for skills that can sometimes stand in for Influence skills:
- Administration uses the tool of officiousness: "Do what I say because I'm up the org chart from you and filed a Work Order."
- Carousing uses the tool of camaraderie: "Do what I say because I'm awesome good fun!"
- Law uses the tool of legal repercussions: "Do what I say, or I sue you or make sure you go to prison."
- Merchant uses the tool of assets: "Do what I say because you'll get rich, not get poor, or get something physical in return."
- Leadership uses the tool of loyalty: "Do what I say for the good of the Corps."
- Politics uses the tool of influence-trading: "Do what I say because you want my support when the time comes."
- Public Speaking uses the tool of haranguing: "Do what I say because of this lengthy list of reasons in favor of my case."
In all cases, "what I say," isn't pivotal to the skill but to the specific use of the skill. Bad matches can give penalties, sure, but won't make the skill inapplicable. The same goes for emotions . . . mind-poisoning hate speech, scary lies, threats of legal or social action, threats of withheld sexual favor, violence, and even dumb party tricks ("Let's light this 151 on fire!") can evoke fear. For that matter, being attractive, forceful, fun, important, or a silver-tongued liar can all evoke lust. Granted, some uses are inappropriate (using Leadership rather than Sex Appeal to get sex, using Intimidation rather than Law to cause a witness to cave in, etc.), but again that's grounds for a modifier, not for forbidding the use.