So, It's been years since I first played and watched the Danganronpa series, but recently my interest in the series has resurfaced. As such, I decided, why not insert Shirou into Danganronpa, and see how things go when he's introduced to the series?
The reason why there are two different titles for this idea is because they both refer to different ideas for how this crossover might go. The first idea will contain the majority of how I want this to go, because I can't do as much with the second idea.
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I'll start with the first idea. This idea is to make the worlds of Danganronpa and Fate coexist. Magecraft would still be a thing, as would the clocktower, but Hope's Peak Academy and It's Ultimates would also exist separately. In this idea, Shirou would be scouted for Hope's Peak perhaps before the Fifth Holy Grail War, but then actually attend after the events of it have already taken place.
He should be the Ultimate Hero, Helper, Justice, or something along those lines. Despite this, I'd also appreciate it if you referenced his archery skills somewhere down the line, mentioning how Hope's Peak thought about giving him that title too, before he stopped being apart of the archery club.
In my opinion, there's not much that can go different from canon in Danganronpa unless Shirou already has some more-than-basic capabilities in his magecraft by the time he enrolls to Hope's Peak. Otherwise, it'd be just the same as adding in a new character that's only there for the sake of being there. The Unlimited Blade Works route would work best for this story, since the Heaven's Feel route would make any Ultimate title Shirou could gain invalid, and Fate route Shirou has barely any of the magecraft capabilities he would need to make a difference.
Since it's a combined world, some things will need to change to accommodate that. One of these things is that Junko Enoshima needs to have knowledge of magecraft, and a large amount of capability in using it. She should teach the Remnants of Despair their own unique magecrafts, as well. This is all because that otherwise, there's no way the various magi of the world would allow society to collapse the way it does in canon Danganronpa.
The spread of despair would be defeated all too easily if her and the Remnants used only mundane means to accomplish their goals, and if they used magecraft to only a small degree, they'd still lose. A solution to this is to give everyone magecrafts corresponding to their Ultimate talents.
Junko and the Remnants would be the only ones to know how to use magecraft at first, (Nagito would be a particularly interesting case in that scenario, and I imagine It'd be a lot of fun to write whatever nonsensical things he can pull from out of nowhere), but later on Class 78 could learn magecraft while they're trapped in Hope's Peak, via Monokuma revealing it's existence and how to practice it to them, and by proxy the world, since it's being broadcast.
The murders and class trials in general should go a bit differently than canon, with the addition of magecraft into the mix. Don't change the victims or the culprits around, though.
I'm still unsure of the details of how I want this all to work, but in some way I want Shirou to save Chiaki, (the real one from the anime), and for Hajime to only be half turned into Izuru Kamukura before being saved. (He would have some Ultimate talents, but not all of them to the point of being bored of everything or completely logical. He should also have one red eye like in the anime.)
Since I'm not really sure where to go from here, it's up to you what happens after, such as whether Shirou participates in the killing games of Trigger Happy Havoc or Goodbye Despair. I also don't know how the whole timeline would change from this, as even one slight change in how things happened during the Tragedy could set off a chain reaction with later events.
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The second idea is for Shirou to get transported to the world of Danganronpa by Zelretch. In this case, I'm not going to go into nearly as many specific as I did in the prior idea. You can either have Shirou's magecraft removed from the situation, and have it so that's he just another Ultimate student who likes helping others, or you can have him be an outlier with his magecraft. Either way, he'd probably be interesting to Izuru Kamukura. In the first case, it'd be due to him wanting to know what drives him to help others, and in the second case it'd be his magecraft.
Of course, you could also go the route of Shirou not being an ultimate at all. It all depends on when in Danganronpa canon you introduce him. Does he get transported before the Tragedy, eventually getting scouted by Hope's Peak for how he goes out of his way to help others so much? Does he get transported during the Tragedy, saving whoever he can, but being too late to save some people? Does he go through Trigger Happy Havoc, or Goodbye Despair? Does he go through neither and just be part of the Future Foundation? Those are your some of the choices you need to make if you're going to be writing this story.