Presumably Hayasaka would have some experience with security as Kaguya's personal attendant, and the team of people she asked for would also have some training, but yeah this strains credulity unless Un'yo's position is so bad that he is almost completely out of options.
Yea... that entire arc was stretching the truth like glutenous dough. But it made for a fun and satisfying adventure. In reality, the only way to keep him safe would be to find a way to make him being alive more valuable than him being dead. These global monsters think in decades and percentages... to them Kaguya is a valuable tool for asset acquisition and conflict deescalation. Her worth is probably in the billions to them.
Both parties would find matrimony between and heir and a young lady of their respective families auspicious. Conflict is expensive, and unpredictable.
It's good for the Shijo's, because it allows them a 'backdoor' into the Shinomiya group, going the slow and deliberate waylay weaving knots around the Shinomiya family. They would likely begin a directorship merger, Cross-shareholding and voting bloc momentum (both families authority (leaders, directors, the board.. etc) would share in voting rights). Then the Shijo's could slowly push for greater share purchase, greater veto power in key decisions through Shinomiya's bribable board members, strategically place trusted shareholders in favourable acquisitions and stocks. They would likely put more purchase power behind trade deals with other companies that favour the Shijo's ethos, or whatever else. There are countless ways to slowly incorporate the Shinomiya wealth/family into the Shijo conglomerate.
It's good for the Shinomiya's, because it gives the temporary respite. They're in more shit than the Shijo's, because they have less unity, more internal disputes, they are the ones being 'attacked', so they'll be on the 'defensive' most likely. Not to mention, the Shinomiya's are corrupt, which means there are countless malpractice, personally incriminating evidence, voided regulatory fines and other dark marks that the Shinomiya's have paid great expenses to hide. But throwing a blanket over something doesn't make it go away. It's only a matter of time and investigation before each dark truth can be harvest by the Shijo's. For them, marrying Kaguya off buys them the time to recapitalise, restructure and cover-up... or to put it blankly... like their wounds. They'll most likely use the marriage as a shield... other companies seeking to pick up the scraps from the Shinomiya's fall will be deterred as it now means implicating the Shijo family as well.
All in all, this kind of political marriage is/was quite common, it benefits both sides, so neither would be opposed. The heir of the Shijo's (forgot his name) is mostly just a figurehead, as a teenager he'd hold very little sway in his family. He's just a puppet for the board/council and reigning family heads to manipulate and use. It's not at all like it is portrayed here, both he and Kaguya would have little to no say in this marriage, as it's something both conglomerates would unanimously agree on.
The thought that a group of teenagers could somehow come out on top if slightly contrived. However, I can definitely imagine that if they could convince their parents (all people with strong political sway and capital) that interfering in this marriage is profitable, there's a chance they could instigate a commotion. If this were more realistic, it'd most likely be the kids pleading their parents to have the Shijo and Shinomiya's renege on their union. For third parties, there is definitely profit to be had if a decaying company with corrupt, hidden scandals is brought to its knees. Not to mention, the Shijo's wouldn't have the capital to collect the most spoils, or the gal to offend other large companies for risk of implication and 'ganging-up'. Most likely as soon as this happened, they'd switch to plucking the lowest-hanging fruits and then cut down the tree, leaving the others to scramble for the fallen fruits.
in conclusion, it is plausible (though highly unlikely) that a small group of teenagers could ignite the fuse of the bomb that dismantles this arranged marriage and have the two main leads live happily ever after. But there would be a host of consequences that I can't even begin to name that would come from that. Kaguya's best bet is to record her brother threatening her, and other things going on in the house and feign mental instability (Though this is dangerous, as Japanese families are highly concerned with bloodline and purity, and so she might just be erased for good).
This could buy private investigators the time they need to uncover enough court-proof evidence to dismantle or at least thoroughly shake the family. She could then counter the brothers threats with this information and her own recordings... though this could backfire if not done well enough. Another, though highly dangerous, option, is to wait until the day of the wedding, then during the ceremony release all incriminating evidence, and play the recordings on the speaker of the brother's threats. It would most likely be a high-profile wedding. Such a sudden burst of legally damning evidence could cripple the family. And the Shijo's would almost definitely not go through with the wedding to save 'face'.
If done well, she could seek shelter under the might of the Shijo's or another powerful entity as she rekindles her romance with Shirogane. But in all honesty, she spend her life living in fear of retribution from her family. Though, her best bet would be tone 'invisible'.
At the end of the day, if this were reality, this would most likely only go one way: Shirogane has no influence whatsoever, and his friends wouldn't either. Kaguya would resist for a while, but ultimately, her effort would be snuffed out under threats. She'd likely marry the Shijo heir, who would also have no say in this. Both would live a miserable life. They would likely come to resent each other, their companies and families, and this hatred would only further infect future generations, and make them more likely to act as their families do. The only realistic option I see: the Shijo kid and Kaguya 'pretend' to be a married couple, whilst she retains her relationship with Shirogane as 'a lovers affair'. The Shijo kid could find love elsewhere. Though, being such high-profile characters, this affair would be difficult to conduct, and it would be pretty much impossible to have a normal family life together unless they wait a decade, watch their families decay (maybe even silently instigate). They could slowly dismantle the Shinomiya family, and then divorce. That's my realistic possibility in which Kaguya and Shirogane could be together. But even then... it's a teen romance... if this were real life, they'd probably be over it in a few years, and the two seem compatible at least from what we've seen. But it's all just messy, complex and contrived.
But yes... I might be repeating myself too much here,
but if this were to have a happy end. The wedding would have to happen, Kaguya and Shirogane would have an affair, the Shijo kid and Kaguya would need to find ways to instigate a 'window' through which Shinomiya could escape the marriage. This would buy them years of time and opportunity.