This request really isn't easy. I racked my brains the first day and I still haven't really thought of anything that fits the description.
Isn't part of the problem that the whole point of an idiom is that it uses words in a figurative sense rather than a literal one? When you, say, rack your brains, you don't literally torture your brains on a medieval device -- you just think hard, but how do you act out that specific sense of thinking hard and not some other way of saying the same thing? If you're doing charades and you manage to imitate, say, Rodin's thinker, everyone will just say 'Think!' 'Thinking!' and no one will say 'Rack your brains.' But if you try to act out a rack, whether it's an oven rack or an instrument of torture, I'm as skeptical as Norbert is that anyone will get it in any reasonable length of time. For most idioms, I don't picture a class full of language learners finding that approach very helpful. That's why idioms are usually things that you just have to learn.
But for some things, like, say, parts of the body, there might be exceptions. I looked back in this listSiehe auch: "Real" friends??^ - #170
and thought there might be a few there you could work with, e.g.,
welcome so. with open arms
an ace up one's sleeve
roll up one's sleeves
have both feet (firmly) on the ground
have one foot in the grave
the penny dropped
throw in the towel
wash one's hands of sth.
But even there, several would need props, or might be more suited to drawing on the board than acting.
I'm really curious now whether you found any that do work.