Despite the user accessible screws on the back, you should not take it apart.
Now that’s out of the way, here’s a picture of the internals of a Chameleon IHD3-PPMID (CA30117 Type 1)
The internal battery is 200mAh which, according to the booklet you should receive along with your new meters, will last you about an hour and a half. Enough time to carry the IHD somewhere else to check consumption (but not too far mind you as the wireless range on them is pretty poor) and then plug it back in again.
The gold pads in the middle connect with a spring on the back of the case as an anti-tamper switch.
If you take your device apart, it may cease to function properly/you may need to pay Bulb for a new one.
The USB port has pads for (presumably) direct connection to the main microcontroller for programming/direct data access, but this section remains unpopulated on consumer units like this.
If I get a bit of time, I’ll remove the RF can over the interesting bits, desolder the main board from the screen mount section and probe around a bit with an oscilloscope to see what I can find.
If any data is accessible on the device locally, it potentially would be possible to cut a hole in the back of the case, solder the anti-tamper pads together and then remove the back to have a play but I really wouldn’t recommend it.
If you want to wall mount the device, removing the casing to just revel the screen in some way (and remove some bulk) is also not possible without triggering the anti-tamper so I’d recommend a 3D printed case that fits around the existing one, and a right angle USB cable.