OP, I don't want you to feel like I'm trying to tell you you're mad, but from your posts I get the sense that maybe you've conflated 'hand in mouth' with 'E.Coli'. You're seeing the risk being the behaviour that is likelier, rather than the risk itself, that is less likely, if that makes sense? It's really common - we all do it, and about positive things too.
Basically, you seem more worried that she will put her hand in her mouth, than worried that the hand might have E.Coli on it, if that makes sense? But actually - even if she DOES put her hand in her mouth, it's only a tiny chance that it will have E.Coli on it to begin with. But you can focus on the hand, rather than the invisible and undetectable bug.
So for you, of course it seems worrying! Because kids DO put their hands in their mouths, and you're right - even with 1:1 it's impossible to be certain they won't.
Again, I think you should do what you feel is right, and it's not a big deal, but I would encourage you to consider that statistically, the risk of your DD putting her hand in her mouth with dirty hands is not too massive (as you said, it's a good childcare centre with good staff who will no doubt do their best) and the risk of said hand having E.Coli on it is very very small.
My stats are not the best but I did some numbers and they could be wrong but I THINK, I did a sum where if your daughter normally has her hands in her mouth 10% of the time (ie a solid 2.4 hours a day) and your petting zoo trip is 3 hours, 1.5 of which are spent with dirty hands, then I THINK the risk of hand going in mouth (leaving aside the idea that a supervisor might stop her) and said hand having E.Coli was about 0.000024, which is, to put it in context about 10x less likely than a single dealt poker hand containing four of a kind.
Yes, it happens. And my sympathies are with anyone it happens to, the same way they are with anyone whose kid comes to harm in tragically unlikely circumstances. But it is very, very, very unlikely, and most people will not see it as risky enough to warrant taking action over - I guess for the same reason most people let their kids ride bikes, or go to amusement parks, or ride in cars. Because for them the risk/reward is worth it.
But if this is your 'one thing' then I think fair enough, everyone's got a 'thing' (I refuse to own a microwave. I know, I know I'm mad. Evil rays! Evil rays!) and your daughter will grow up and then if she wants to she can pat all the sheep she wants. It is not a big deal. BUT - it is a tiny, tiny risk, and I just hope that this IS your 'one thing' and you're not worrying yourself to distraction about all the other tiny risks. Because I do think that's not great - for you or the kid!