1) Use single-edged razor blade to separate the top (red) and bottom (white) halves of the sensor casing. There's probably a way to separate them more cleanly than I did, but I just ended up cutting the two halves apart. No biggie, I'll glue them back together later.
2) Disconnect the leads to the battery. There are two wires that connect to the top of the battery, white and black. They're soldered in place, and there's a bit of glue over the top of the solder. I used a scalpel blade to remove the glue and a soldering iron to remove the solder. This was some heavy-duty solder that wouldn't melt until I cranked the heat up over 800 degrees.
3) Pry battery out of casing. The battery itself is a typical CR2032 3.6V Li Ion battery, which can be found at any battery store. There is double-sided tape sticking the battery to the white half of the case. I used the back side of my scalpel blade to pry the battery out.
4) At this point, the battery is still connected to the circuit board by two other wires, red and black. I've unglued and desoldered those wires like the previous two, but now I'm not so sure if that was necessary.
5) Buy new battery. This is the step that I'm stuck on, since I'm at work and just started this today. When I get the new battery, I'll know if the second set of wires really needed to go. Either way, from here on out, the process will just be the previous steps in reverse order - solder the new battery in place and glue the casing back together.
All in all, this has been a pretty easy job. Of course, it was made easier by the fact that I had nothing to lose since the sensor was already dead. Also, having the right tools handy certainly helped:
1) Single-edged razor blade
2) #11 scalpel blade
3) Soldering iron
4) Some fine forceps to help maneuver the wires during soldering/desoldering
5) Microscope. This isn't necessary, but the solder points are really small, so magnification (10x) was a definite plus.
I'll post when I'm finished to let you know if the process was a success.
<Edited by Moderator>