Before I attempt to open up devices I always like to take a look at some pictures so I know what to expect; for the Empatica E4, there weren't any online anywhere. I went ahead and took some in case anyone else wants to replace the battery without shipping it to Italy.
The mechanical design is nice, I think the castellated addition for the optics is a great idea, and they have some nice spring loaded connections to handle the geometry of their sensors. There are two Microchip PIC24Fs as the main MCUs and it uses the silabs BLE112A for comms. It'd be fun to spend a little more time digging into the design, but I'm strapped for time at the moment; maybe in the near future.
For me, the goal was to get my failing one back up and running after what appeared to be a simple failed lipo battery. You can see in the pictures the battery is bulging; you can also see they use the straight up cell without the normal protection circuit that comes with many off the shelf lipos. I ordered a replacement 300mAh battery and soldered on this JST SH 1.0 Connector and it worked no problem after a little fiddling (gotta get the fit right, the had some uniquely thin 300mAh batteries– and that lack of a protection circuit helps with the size).
Anyway, here are some pics; sorry they're not top-notch, my microscope is packed up for my upcoming move.