Well, my issue is that I'm not very familiar with either the characters, or the specifics of what is and isn't allowed for the match. Going strictly by the rules set, for example, Shirou can't use Avalon even. At all. Which might pretty heavily impact his chance of winning? I guess I'll look anyways-
While Shio seems to have a magic-resistant dress that can potentially work like armor/an insulator of sorts against Natalia and Kiritsugu, her weapon Golden Excalibur doesn't seem to have that same protections, so there's nothing stopping him from Tracing it and getting a copy of its own, complete with the blade beams, Attack Power halving, all the bells and whistles. So, with both character's attack powers halved by the other's Golden Excalibur, the fight is prolonged quite a lot. Who benefits most from having the fight so prolonged? The one with the instant-kill move- that is, to say, Emiya. Even assuming Shio's dress can absorb the magic some, that doesn't mean that the entire rest of Shio shares that protection.
The main other point against Shio from what I can see is that, in spite of all of those supposedly perfect heroic genes given to her, her intelligence is... not great. If Shirou gets any kind of inch at all to breathe and think things through, he's going to use it far more effeciently than Shio would to come up with a battle plan.
Really, what I think it comes down to, is just whether Shirou gets the needed hits in with Time Accel before Nuclear Jutsu kills him, since basically every special defense technique he'd use to stop it- Rho Aias, Avalon, et. al.- just kinda stopped working. For someone who actually knows how to fight in those circumstances, against someone with all-seeing Demon Eyes (and thus can't be hidden from), the only really viable strategy is an aggressive one, so I think that's more or less what he'd do after evaluating the situation. There's not really hiding from Shio, but since they have a fair bit of starting distance, and SBA sets the fight in Central Park, there's at least some general stuff in the way to help out with getting into melee range.
TLDR: Even without basically half of his powers (ex. Unlimited Blade Works, the aforementioned defense techniques, etc.), if Shirou doesn't immediately get caught full-on in a Nuclear Jutsu and explode (which seems unlikely given the battlefield isn't a perfectly flat plane), he probably wins via Tracing/Intelligence advantage/Time Manip.
