Learn English – A word for something that’s done only half-consciously

Browsing through COHA and Google Books, I can’t find any body parts that can be shrugged apart from shoulders. In any case, the intransitive use — she shrugged etc. — is certainly always understood as the shoulder-gesture — it is, as you say, essentially redundant.

So shrugged is very nearly a stormy petrel. The only other thing you can do with it (that I can think of or find in the dictionary) is to shrug something off.

(If anyone at a subscribed university or library is reading, by the way, the OED online would be my best bet to look for other usages — their historical quotations will hopefully show how it came to be used this way. Unfortunately I’m currently travelling and so without access. Also, a clever COHA search would probably be able to automatically look there for instances of anything non-shouldery being shrugged, more thoroughly than I could browse.)

You are right that ignorant/ignorance often carries a negative sense ("He's so ignorant!"), but it can also be used neutrally ("Ignorant of what had happened in my absence, I continued as before"). It can certainly be used to express humility ("Forgive my ignorance, but who is the current president of South Korea?").

For the neutral sense there is also unaware (and unawareness).

There are not many emphatically positive expressions for lack of knowledge, since this is usually considered a negative (though you might argue innocent has this sense; also ignorant and unaware are often combined with blissfully, after the proverb Ignorance is bliss). But there are expressions for situations where lack of knowledge is expected, and therefore perhaps less negative — for instance, novice, apprentice, learner, beginner, and if your aim is to express humility then any of these would be appropriate.