Actually, I'd say that, if anything, Ilya is a bigger issue than Sakura is. Since he has no connection to Kiritsugu here, Ilya will have no reason whatsoever to care about him, and thus will not follow him around in the way that she did in FSN. Further, she actually seems much more aggressive and involved in the war than Sakura would, and thus it would probably be less obvious that there was anything "wrong" with her. And, of course, there is the additional problem that she is the Grail, and thus for Shirou (or anyone else) to obtain it she has to die. Now, I'm not saying that he'd kill her (it seems unlikely to me), but someone like Gil sure as hell would....
As for Sakura being passive, you're probably right there, since she has neither the ability or the motivation to get involved in the fighting, but at the same time she has nothing much to live for, so she's not going to be overly interested in protecting herself either. If she came up against a master or servant who was genuinely trying to kill her, she would probably not last very long. Of course, fortunately for her, there aren't any masters who would be genuinely trying to kill her (Rin and Shirou wouldn't even consider it, Caster is entirely defensive, Kotomine couldn't give a crap about her and Ilya would just smash through Rider if they ever fought), so....
Another thing to consider is Dark Sakura, the shadow and the like. I believe that Zouken's original plan for Sakura was to have her absorb the servants and become the Grail (certainly, the way he talks to her in the HF interludes implies this, because he says that he wanted her to "capture" the servants). This didn't work canonically because she was unwilling to fight, but here it could quite easily happen. And, if it did, there's a high chance that the shadow would come out, like in HF.
What Sakura would do in a war like this is actually a very good question. She doesn't seem to me to be the sort of person who would really put much effort into it (like Ilya, in fact, if you take Emiya Shirou out of the equation), but at the same time she has got to do something. Possibly, like you say, Rider would basically fight on her own, for Sakura's sake. That does, however, make it hard for Shirou to find out the truth about Sakura.
Personally, I would say that the best way to get Sakura involved is for him to do research into the Matou family (as well as the Tohsaka family, probably) as part of his planning for the war (since they're both known participants). It's simple common sense that you would want to know who your enemies are, and I would imagine that the TSAB would at very least have enough resources to discover that Rin is Sakura's sister and that the Matou magic is somewhat dodgy. Given that information, he likely has enough reason to look more closely at their situation and to attempt to resolve it, especially if he asks Rin about it at some point.
Another possibility is for him to look into alliances. I can't imagine that even TSAB Shirou could take Berserker alone, so anyone he can form an alliance with would be very helpful. Most likely, that would be Rin, but Sakura would not be an impossibility, since Rider has no real chance of taking down Berserker on her own (I believe). Once that happens, of course, him finding out the truth about her becomes much more likely.