If you take your Swiss Army watch to a jeweler or watch store every time you need a battery change, you may spend several dollars each trip. But if you're more of a do-it-yourself person, you could invest in an affordable Jaxa wrench and watch case holder to save a little more money in the long run. In order to remove the back of a Swiss Army watch without damaging it, you will need to use these specialized tools.
Anchor your watch case holder. Most watch case holders have adjustable clamps that you can use to mount them to the edge of a work table, just like vice grips. There are a few other styles, such as those with rubber bottoms that are designed to grip your work surface. Make sure your case holder is stable.
Loosen the case housing of the case holder. The case housing is the part that actually cradles the case.
Put the Swiss Army watch case face down in the case holder, then tighten the surrounding screws to lock it in place. When all the screws feel finger-tight, try to wiggle the watch head and the case holder. Nothing should be able to move.
Install the flat-sided bits on your Jaxa wrench, then place the bit-side of the wrench down onto the back of the watch case. Turn the wrench as needed to get the bits to line up with the flat, shallow grooves on the back of the watch case.
Turn the wrench to the left, applying gradual but firm pressure, until the watch back starts to turn. Continue turning until the watch back either pops off or becomes loose enough to finish unscrewing with your fingers.