Use paper stickers with housekeeping information to keep track of your disk drives!
How would it help? Well, the stickers can have flat coils inside, just like those stickers that make detectors at shop exits beep at you. The coils can do the EMP and degaussing stuff, while also doubling as an antenna for a small control chip. That tiny low-power chip, and the coil, can be powered from a relatively small capacitor, which can be hidden under the sticker too. (Or inside the case, in case of SSDs, as those rarely have big enough cavities on the outside to hide the capacitor in.) The capacitor is absolutely essential in the case that the disk is completely disconnected for maintenance or other reasons when the kill-switch is triggered. It is recharged when the disk is online.
Sticking that coil right to the disk's circuit board should allow for small enough capacitor to kill whatever chips are on the other side with EMP, or to degauss the platters. For SSDs that extra capacitor can also be connected directly to the board instead, frying all the flash chips as soon as the signal comes. Maybe that small controller could also be connected directly to the motor and the heads of an HDD, making it literally scratch out all the data by slowly spinning the platters under unparked heads.
Add a powerful enough wireless transmitter to cover the whole complex, and a big red button (or a small gray one) for the trigger, and you are set! Keep in mind, though, that if someone tears off a sticker and notices a capacitor that's not connected to anything, they might suspect something and take a closer look at the sticker... With that caveat in mind, I think the idea is quite plausible. Someone might have to figure out exactly how big the capacitor has to actually be, but at least for frying flash in SSDs you most definitely can buy powerful enough yet really small caps.
My original idea follows:
Software could, and would in the context of the story, be found and purged.
What about embedded software? Modern computers are very damn smart. Every sizable component has a CPU, be it a network adapter or a microSD card.
Intel AMT allows you to connect to a server remotely and work on it like it's in front of you: a display, a keyboard, you can even "plug in" your hard disk into it over the network. And the best part is, all this works as soon as you press the power button (some of it even before that), and it is completely out-of-band. That last bit means that any software working on this server will never see any AMT traffic, and it will think that you've actually opened up the case and attached that HDD.
Despite having all that functionality, AMT works almost entirely on the motherboard itself, doesn't touch the main CPU or RAM, and is almost invisible to the "main" system. It's code is very obscure, extremely platform-specific and proprietary. Only some very smart hackers managed to get into it (and find a few glaring security holes...), under the normal circumstances no one will ever touch it in any way other than through the official client software from Intel.
Every HDD and SSD has an embedded controller, too. Wiping an SSD "from the inside" is as simple as "forgetting" where the index for all of its flash memory is, maybe wiping that relatively small index beforehand for good measure. And on HDD you can just slow down the platters enough for the heads to land on them and dig trenches all over the surface. (The heads are too weak to magnetically damage the data quickly enough, so physically damaging the surface is the only way.)
All the network hardware also has embedded processors, even the "really" embedded ones in case of bigger devices that are like normal computers themselves on the inside.
What I'm getting at is, most people don't even realize that their microSD card may well be more computationally powerful than a PC from late 90s! No one ever really looks inside those embedded chips. Oftentimes you cannot even read the firmware from them, only flash the updates. (And thus their security is severely lacking oftentimes, except the "Security through Obscurity" kind.)
If some kind of backdoor is installed on that level, I doubt that anyone will ever notice it. At least not until it's exploited and forensics start digging into the chips. No "normal" software will be able to detect that something's wrong, you'd have to take the device apart and dig in with a JTAG debugger to even have a chance.
Let's say that one of the routers in the datacenter receives a malformed packet. It looks like it's a normal packet that got (unnaturally severely) corrupted in transit. Normally, it would be silently dropped, and higher level protocol, like TCP, will request retransmission. Suddenly, the router broadcasts that same packet over all its connections, and then immediately "dies", maybe requiring a firmware recovery procedure to continue functioning. Every server that receives the packet suddenly crashes due to CPU voltage dropping below acceptable minimum, and its disks experience catastrophic firmware failure that destroys all the data in a matter of seconds. A few more seconds later, the "smart" power supply infrastructure, which also received the packet of death, cuts the power to the whole complex. And perimeter routers just receive and drop the packet as they should, not a single bit of suspicious data gets outside.
In just 10 seconds or so, the datacenter inexplicably goes from perfectly fine and healthy to totally blacked out and dead. All the networking infrastructure is lacking any firmware to even work. All the data is lost, either in unintelligible fragments randomly scattered across several flash chips in each SSD, or literally scattered all over the insides of HDDs.
No one has any clue as to what has happened. Even if someone figures out later that the firmware of almost everything in the complex had peculiar bugs that just so happened to act together in such devastating manner, it can still look like it all was an accident. Since there are no traces of the packet that caused the whole mess, the only way someone might figure out that it was malicious is by contacting HDD vendors and finding out that the firmware slightly differs from what should have been there, but even that would be practically impossible to say for sure, due to how much things change internally during product life cycle.
And in that last bit lies the catch. That 'small team' of yours will have to reverse engineer the firmware of every HDD, SSD, motherboard, network card and router in the datacenter, plus the smart power supply system. There likely will only be just a few kinds of each component, since they are ordered in bulk, and the slight variations in hardware revisions should not be much of a problem, but that's still a huge load of work, and it will take time.
Plus, if any machine just so happens to be offline, as in "completely disconnected", its data will survive. The same goes for any disks that happen to be taken out at the moment. The only "safe" solution to that would be to have a small autonomously powered wireless bug on every HDD that will, when triggered remotely, turn on the disk, if it was offline, and order it to go kill itself. Or make it discharge a capacitor into a small flat coil glued to the disk. (Like those stickers that make detectors at shop exits beep at you. It can even have some housekeeping information printed on it, so that there is a reason for it to be there. No one needs to know that there is a coil inside the sticker. The capacitor will still be noticeable, though, unless you hide it under that sticker.)
Or, you know, you could just kill it with fire. But that is outside of my area of expertise.