How do I find this thing that I don't know what to call?

Like this ?

@thorninmud had one good suggestion. Another might be simply installing something like a smaller-sized shower grab rail over the button, which would allow instant access to anyone who needs to press it, but helps to avoid casual contact. Another benefit of such an installation would be that it would be pretty sturdy.

I was going to suggest an electrical breaker box enclosure but after reading the two answers above I changed my mind. You want to be able to shut the machine off in an instant. That means the switch needs to be visible and accessible immediately. The grab bar will do it.

How about a shroud like THIS?

Why not just have the button moved to somewhere more convenient?

I expect that the location of the button is required by code or by law to be “convenient” to the user of the machine or to people in the room. I suspect that’s part of the problem that @syz has: The location is also convenient to people who happen to be in the room, but who aren’t operators. In reality, your solution would be to move the button to a place that’s “less convenient”, so that casual and non-employed persons in the room wouldn’t accidentally trip it. But emergency shutoffs generally have to be “convenient” by being “easy to reach”. That’s the main problem here.

Like a button protector?

Like this?