The security token is not designed to be taken apart.

Inside the SQEX token is a CR2032 Lithium cell that is in a standard slide-in contact retainer. While these batteries are easy to find, the token cannot be opened without mangling it (or sawing it carefully to separate the two halves.

Even if you do manage to open the token, you CANNOT lose power to the device, so a simple battery swap will not work. I was careful enough to apply the necessary 3V across the contacts via a current limiting resistor as I removed the cell, verified that the token was still alive (responding to button presses) after removing the battery, and then I slipped in a new one. Alas, it was all for naught since the battery had already drained low enough to cause a reset of the device. This would be a viable solution if the battery health was known in advance, but there was no warning that the cell was nearing expiration.

I just got ahold of SE's EU support, but they told me that I had to contact NA support despite the fact that they use the exact same ticketing system and ticket numbers. Massive disappointment. I guess i have to try my luck with the NA line again in 5 hours.