Imagine a Shirou who was healed without Avalon, and whose Origin is Fire, which is most likely his element, as well. He still develops a Reality Marble, but it looks like an eternal conflagration. The Great Fire of Fuyuki still burns in his soul
He was saved from the Great Fire by a minor magus, a mere formalcraft user with less than twenty magic circuits. The one who saved him nearly exhausted himself keeping the boy alive long enough to reach a hospital, but it was enough. Shirou was saved, and the person who saved him, adopted him.
I've been considering the idea that the person who saved him might have been a relative of Sajyou Ayaka, perhaps her father, and did not so much formally adopt him as become his guardian, with the hope of arranging a marriage to her. That requires knowing that Shirou has more magic circuits than one would expect, though. If the magus does find out, there's still an issue he hadn't considered: Shirou thinks of Ayaka as his sister, not a potential wife. Maybe they should have explained things when he was brought home.
Was also thinking that the magus, whether a Sajyou or not, was an employee of the Fujimura clan. A man who joined the yakuza to help his community, and sees it as a true chivalrous organization, not the group of violent thugs many outsiders and police consider it to be. Of course, Raiga certainly encourages that belief. This Shirou could still wish to be a Champion of Justice, but would have a different (though clearer) idea of how to go about it.
Shirou's training in formalcrft goes well enough, but he lacks canon-Shirou's talent for Projection, and thus, has to use real things as sacrifices, rather than Tracing them. His true talent lies in Fire, both its its destructive and creative aspects, and while he can use formalcraft to convert it to other elements when he has time, any magic used in a hurry (like, say, combat), without a Mystic Code or Conceptual Weapon, is going to be Fire-based. I'm not sure how good formalcraft is at creating Mystic Codes, as the wiki doesn't say, but as Shirou is capable of using Fire's creative aspect, he should be able to forge Mystic Codes, but would have difficulty crafting any that did not involve Fire in their creation. Conceptual Weapons are probably right out, though he might have a small chance of obtaining one through other means.
I do not have an Aria for his Reality Marble, though I do have a possible name for it: Birth of the Phoenix.
One may wonder what happened to Emiya Kiritsugu, that he was not there to save Shirou. Perhaps he found someone else to save, but that involves either creating a new character, or changing the story of an existing one.
One possible point of divergence for this is that Tohsaka Sakura was not given to the Matou family, but to another. Let's say, a childless couple who use crystal magic, something similar enough to gem magic for Sakura to perform more easily than the Matou style. This Sakura, while still a very nice girl, has a much better sense of self-esteem, and occasionally shows an impish sense of humour, such as teasing Rin about Shirou by calling her 'Tsundere-neechan'. She may or may not even live in Fuyuki, or be interested in Shirou beyond 'nice, handsome guy', and might not be chosen as a Master. Perhaps the couple is more eccentic (from a magus's perspective), and Sakura is developing technomagic. (Weird idea: Babylon 5 came out before the Fourth Holy Grail War, so Sakura could be a Technomage fangirl, with a stylke to match.)
Another idea is that the couple or person she was given to was killed in the Great Fire, and Kiritsugu saved her, thus explaining why he didn't find Shirou, since her was busy saving Sakura. Not sure how plausible either option is.
Either of the above would mean that Matou Kariya had no reason to enter the Fourth Heaven's Feel, which would change that War severely. Tokiomi might not even be dead, and Aoi might be sane. Also, someone else would have summoned Berserker, and would most likely have gotten a different Berserker, at that, which means the Great Fire might not have happened, at all. So, perhaps 'Sakura goes to a family other than the Matous' should have its own TL, where first the alternate Fourth Holy Grail War is played out, then the interbellum decade, and only then the Fifth. Moving on:
Perhaps Kiritsugu found no-one to save, in which case his future might go along the lines depicted in Tainted Ideals, which I probly shouldn't spoil by explaining. There are two possibilities: either he makes it there alive, or he doesn't, and that's going to strongly affect how Saber's Master behaves.
Its also quite possible that he dies in the fire, and Avalon is either lost, or found by someone else, who will most likely be Saber Arturia's Master in the Fifth Heaven's Feel. Having that person be Shirou is out, as that strains SoD too far. Rin, perhaps? Maybe she found it during the time before the Fifth, or maybe Kotomine found it, and thought it would be amusing to give it to her. Maybe Ayaka or Sakura has it, and angsts over having to fight Shirou and/or Rin. Maybe Mitsuzuri Ayako has it, and is even less prepared for Saber's arrival than canon Shirou was. Maybe its hanging in the Ryuudouji Temple, and Caster uses it to summon Saber.
Maybe it stays lost until the War begins, or isn't in the story at all, so the Saber of the Fifth War is not Arturia.
I tried to come up with a good Servant for this Shirou, and my mind wandered to Azula, and from there, to this odd idea: Avatar: the Last Airbender, the cartoon, is in this version of the Nasuverse, a distorted account of events that took place in pre-Imperial China, Korea, and Japan, during the Age of Gods. Caster (or Berserker) Azula is pretty much the person she was in canon (maybe more sane, maybe less), and might have the ability to summon other spirits attached to her Legend - or not, considering that they abandoned her at the end. Depends on how close the end of the series is to what 'really' happened in the Nasuverse, and whether they got close to her again, after. Using Azula saves the trouble of creating an entirely new character, but if there's a canon Nasuverse character that would fit, the author is certainly free to use them.
EDIT: You may want to ignore most of the first four pages of this thread. Sorry.