In all likelyhood the flashbang armored ninjas with automatics, night vision, "get the fuck on the floor and shut the fuck up bitch" entry will happen while you're asleep, so you won't have time to hit the big red button anyway.
Take a relay and connect it to a door switch. When they open the door without authorization[1], the power to the machines is switched off. Then the ninjas' with their typical noisy entry will switch off the system themselves, without you having to touch the Red Button. [1] can be an ID button, can be a wireless ID token (advantage: the reader and the whole identification action can be invisible), can be a keypad, can be an arbitrary complex biometric ID, or any combination of the above, for a low-tech approach can be a reed relay under the wallpaper and a magnet touched to the given spot on the wall The system can be easily coupled with a common-grade burglar alarm, further increasing the range of conditions the shutdown can be triggered with. (Optionally with several levels, depending on the tradeoff between the recoverability from a false alarm and the consequences of missing the alarm: power-down, erase of a long key (unlocked by a passphrase) from NVRAM, physical destruction of the disk array once forceful penetration of outer zones (triggering sequentially the previous lower events in reaction) is followed by physical breach of the server room door or walls (or the so often woefully neglected ceiling and floor).)
So, the best way to avoid that situation and not being able to reach the big red switch, is simply not to attract their attention in the first place by not following the footsteps of Jim Bell. :)
True. But once the adversary becomes totally information-aware, it will be rather difficult to not attract attention.
A more likely, and far more important, scenario to worry about is the black bag job whereby a hardware keystroke recorder can get installed without your knowledge...
Another reason for employing a security system.
There may be ways to prevent/detect this... Software (open or closed source) alone won't help very much.
May be the crucial part of implementing the security system. Eg, as an embedded system handling signals from webcams, distributed over the building as several nodes (instead of a central one), mimicking the nerve system of insect.