This is excellent! You’re asking the right questions, and giving the right answers, as well.
The basic understanding here is one of creative focus: what is the point of this game we’re playing?
If you’re the GM, your job is to create interesting opportunities for conflict, and opportunities for the characters to pursue their Best Interests. Everything else you do is basically just a stylistic flourish.
When you get to a situation like the one you’re describing, you have to make a choice. You’ve outlined your choices quite well, except for (perhaps) the option of framing straight to the conflict. (I think that, as you probably assumed yourself, skipping over this kind of devalues the King’s stated intent to send assassins and spirits after the adventurer. This is correct; but I can imagine some situations where that isn’t the case, as well. Sometimes it’s more interesting for all of us to skip that conflict.)
How do you make this choice?
In a traditional roleplaying game, it’s often your job to a) present challenges to the players, or b) arbitrate and adjudicate, like a referee, what’s happening in the fiction in a fair way.
In a story-oriented game like this, you don’t need to feel responsible for either of those things. Instead, focus on your real agenda (what I wrote above, and also as described in the thread I just linked to). Your job is to push the Chapter towards interesting confrontations between the main/named characters, and push on the themes in play. Does an encounter with the guards or the assassins do that, or not?
The game puts that choice in your hands; there’s not really a right or wrong choice, except your personal judgement of what would make this Chapter more interesting/memorable, and what would engage the players the most. Choosing one of those as seems most interesting to you is exactly what you’re supposed to do as the GM, here.
Think like the director of a movie or the author of a book: which scenes are going to be more dynamic and dramatic? Which will lead to interesting conflicts between named characters, or affect a major character’s Best Interests? Which are in-genre?
Sometimes it’s quite effective to ask the players, too, because they may have opinions: “Hey, how effective are your assassins? Do you think they really have a chance, catching a foreign barbarian warrior like Hrunk?” Or, perhaps, “How good is Hrunk at navigating these forests? Would a bunch of Royal Guardsmen have a chance to catch him out there, or is it pretty hopeless for them?”
Having said that, there are a few other wrinkles:
First, when we play, we make a point of codifying whether a character wants to have his extended reach function mechanically or not.
Your character can have soldiers and retainers and assassins and what-not, but, by default, they don’t carry mechanical weight. If you want them to, then you should take them as a Particular Strength (and “far-reaching” - that’s what this feature is for).
If you don’t, you still have them… but be prepared for them to be just set dressing sometimes. You can send your assassins out, and the GM can frame around them, or the adventurer can just describe getting past them. That’s the way it rolls.
If you want them to be useful reliably, you should take them as a Particular Strength, for sure.
Generally speaking, we only assign “NPC dice” to someone or something when it’s clear that this character has dramatic weight, potential, and possible Best Interests. Sometimes we didn’t know that when we started playing, and that’s OK. At the very least, they need a name, in any case - an Important Character. Nameless characters shouldn’t waste our highly valuable screen time rolling dice, in other words. (Don’t forget that Chapters are short, and scenes are few… we don’t have much time to waste!)
Would this person be played by a well-known actor, if this was a movie? Are they important, are they interesting? Do they have some agency and interests of their own?
It’s kind of an artistic decision: “Hey, look, at first these assassins just seemed like faceless mooks, but every really liked our descriptions of Moira the Blade, their leader, so I’m assigning her NPC status. She’s cool, right?” “Yeah. Ok!” It’s technically the GM’s decision, but it’s fine to go by consensus or vote or just poll the players and ask, too.
Finally, don’t get too hung up on “dice damage”. First of all, dice damage is pretty rare, in my experience. Usually, the fictional circumstances you’re negotiating for are more interesting to everyone involved, so the “dice damage” rarely actually happens.
If you’re the adventurer, and you’re trying to meet the King, would you rather fight the assassins and have your dice damaged (which potentially means you might have to fight them some more!), or to be taken captive by them and brought to the King?
And “dice damage” can be replenished with each Chapter, if you choose that option. Not quite as scary as it sounds, in other words (especially, as often happens, if you’re not using those stats all that much in this Chapter).
But, second, any dice roll is potentially good for your character, too. After all, you could end up on the Owe List, which is better for you than most alternatives: it’s the real currency of the game, both for your character recurring in the story and for mechanical weight (you can cross it off to get an advantage die against the King when you break free of your bonds and attack him in front of the court, after all).