You don't just shrug your shoulders. You can shrug off responsibility... Or people you dislike... You can shrug up in blankets... You can shrug a jacket on or off...
Right, but none of these can ever be shortened to just
shrug. For example:
A: You can't just shrug off this responsibility.
B: I'm not shrugging!

B: I'm not shrugging it off!
So
shrug by itself can only ever refer to shrugging the shoulders, and not any other body part, and not any of these special expressions. So
shrugged his shoulders is often (though not always*) redundant.
But yes shrugging is fine without specifying shoulders. However there's nothing wrong with redundancy, it's one of the beauties of language.
Good point, but yes and no. Redundancy is often useful, but not always. For example, "to dance a dance", "biography of her life", etc. I agree that it's not wrong, and many people use redundant expressions all the time because that's simply how they learned them, but there's nothing inherently
beautiful about such usage, and if a learner has the option (which the native speaker does not), I'd recommend going with the more succinct form since, stylistically, it's generally to be preferred.
*What Copyright has shown, I think, is that
shrug (by itself) is not only a physical activity, but a communicative one: it means "I don't know" or "I don't care", etc. Thus, a doctor cannot use
shrug alone to command a patient to move his shoulders up & down, because the communicative aspect is missing (only the physical aspect is present); he must instead say "shrug your shoulders", where the use of
shoulders implies neither the presence nor the absence of the communicative aspect. In other words, "He shrugged his shoulders" does not necessarily mean he shrugged disinterestedly/ignorantly; maybe he did so simply to loosen his muscles a bit.