I need to look into my books for any references (which I have source books for every edition) but my understanding over the years has been that minor clans have a school, sure. But while their school techniques might be the same there is absolutely nothing stopping any samurai from learning social skills. L5R doesn't limit "cross-classing" in any fashion. Therefore, even an Ichiro bushi can spend XP on any given High Skill including Courtier or Etiquette unless they specifically take the Obtuse disadvantage. It's not like 7th Sea where you have to level your school skills, or like D&D where you are penalized for branching out. A Hida Pragmatist could spend all of their XP on high skills and still become rank 5 in the school.
Additionally, the minor clans are not just some random standalone faction. Every minor clan is made at home in the lands of a great clan. The Sparrow might have a knack for storytelling and social settings, but the fact is you don't get to stay in the Crane lands by being tactless. Connections are an extremely key thing to focus on. A local daimyo might arrange a marriage to a Doji courtier so that they might handle courtly affairs on behalf of the minor clan.
pg12, Secrets of the Empire
So You've Founded a Minor Clan, Now What?
...Few Minor Clans have skilled courtiers, so finding political allies without overcommitting oneself is the key. Isolation can also work, although this limits the availability of outside resources and trade.
Advantages
Allies: The most obvious solution is to mechanically buy a courtier as your ally to do things on your behalf where they can.
Blackmail: You don't have to be strong or silver-tongued to have dirt on someone. Sure it might come back to haunt you but putting the screws to a courtier can prove lucrative for a one time occasion.
Blissful Betrothal/Imperial Spouse: This is more a roleplay aspect and some GMs might force you to buy your "beloved" as an ally for the effect, but the bottom line is that they will act on your behalf if your spouse has the skills and is in the right places.
Servant: The easiest advantage to justify is to buy an Attendant and/or Merchant. It would be expensive to add Courtier or Awareness to any given servant but it requires the least maintenance in and out of game.
Fame/Social Position/Virtuous: Reputation stats can cover even your bad rolls at times and draw the occasional sycophant to do a favor now and again (I like to think of 7th Sea's reputation rules where your Rep Dice are rolled when you need random recognition or benefactors). In L5R a high enough Honor means you start making the rules because people want to follow your example. High Glory means that whatever you're doing is working so social shortfalls might be overlooked by respect. Status means that no matter how much or little people like you, the honorable ones will still follow because it's the right thing to do.
Gentry: This one more or less falls under the "status" category but if you're custodian of an area, then it is extremely likely that even if you yourself aren't a courtier, someone you have legitimate control over will be.
Different School: Here's the coup de grace. With the right backstory, you might even be able to say that your minor clan character has trained in a Great Clan courtier school. It creates some social dependencies such as fealty and obligation but this is the surest and most direct way.
Character Concept
Imperial. Period.: They might be allowed to keep their clan officially on the record, but being an imperial means access to the imperial courtier schools such as the Otomo depending on the type of world you're running in.
Spider: Being a subvert within a minor clan means that you might even have the Spider clan's
The Mole: Let's face it, spies are everywhere and capable of being in plain sight, even relied upon with enough influence. The right Ninja or Courtier themed spy (a la the Shosuro Actor school from Great Clans 227)
Monk: Being in a clan does not bar you from being in the brotherhood in any fashion and there are several ways to have strong ties within a minor clan's territory and build a social character with the Monk archetype.
Uninitiated Ronin: A well established ronin in a minor clan territory could easily be trained in courtly duties and while they might be disrespected as an emissary, everyone loves an underdog (I would look into the Hawk Purists from Imperial Histories 2, pg103 or Master of Games and Silken Promises Geisha in Book of Air pg179-180)
Specifically speaking about the Fox minor clan, going back to the Way of the Minor Clans it specifically says that the clan has strong ties to the Unicorn due to roots in the Shinjo. It would be very understandable if the allies they have, especially in court, would derive from this clan. Plus, their expansive libraries mean that the minor clan can always leverage important information for equally potent favors. Additionally, if it's modern 4e canon plot then there is no reason a Yoritomo courtier couldn't be an easy fix.
Something quite similar is listed using the Dragon and Phoenix clans in the same book. Stating that if the Dragonfly require anything, the trade or fall back upon their patrons in either clan. It is actually in this section that derives my earlier suggestion for training in a different school.
pg.45 Way of the Minor Clans
The Dragonfly do have bushi. Dragonfly samurai can choose to study either at the Mirumoto or Shiba schools.
I see no reason that principles such as this could not exist for other school types even though it is not explicitly stated (nor rejected). The Tonbo family even starts with +1 Awareness so diverting XP could work easily.