Given the situation in which your Macs are being used, putting the System folder’s permissions safely out of reach seems like a very good idea.
Your assumption about the difference between muting the sound, and setting the output volume to zero, is quite correct. (Although the latter is sometimes referred to as “muting”, it’s really just a kind of simulated mute.) As we’ve now learned, resetting the volume via a script won’t affect the mute setting on your machine(s). But it should override any current volume setting, regardless of whether or not it was previously set to 0.
So, since we haven’t been able to disable mute using software, maybe we should look at some of the possible hardware options. Physically disabling the mute key itself seems like an excellent idea to me (although I hope we can come up with an improvement on the paper-under-key method).
Like you, I’d have serious reservations about removing a key cap from the keyboard. (I’ve no doubt that enquiring young minds would be bound to regard this as an action worth emulating - and, sooner or later, some enterprising little tinker is bound to discover that a pointed object inserted into the gap could still work.)
My guess is that we might be dealing here with the Apple iMac “500” Indigo model (or similar) - in which case the keyboard is likely to be the Apple Pro Keyboard (or possibly the black-key M7803 version).
Many keyboards (including, if I remember correctly, the above models) are known as dome-switch keyboards - due to the type of key mechanism they use. Beneath each key cap is a kind of rubbery-plastic, dome-shaped ‘bubble’. When a key is depressed, a built-in plunger in the dome is pushed downwards, forcing a connection between some circuit-printed membranes within the keyboard. (Subsequently, when the key is released, the dome springs back into shape, returning the key cap to its original position.)
And the point of all this?
Well, if a dome is removed, then so is the functionality of the corresponding key. (If possible, it would be preferable to remove only the plunger part of it - since this should ensure that the key cap is still retained in the correct position.)
Now - I’ve had to take apart one or two keyboards in my time (don’t ask - they’re all long stories). While a good deal of care is necessary, it’s not an impossible task. Rather than take up a couple of pages here, trying to explain the process, perhaps I can refer you to an illustrated article that describes the disassembly of an Apple Pro (M7803) Keyboard in some detail.
Of course, I’d understand if you felt a bit daunted by the prospect of such an operation - even though it’s not quite as difficult as it may seem. Perhaps you know of a tame techie in your area who might be willing to assist? (Naturally, I’d offer to help myself - but I have a feeling that the travelling involved might be somewhat disproportionate.)
Anyway, thought I’d just mention the idea as a possibility…