You don't need a special tool to open a screw back case watch. Just one of these.
Step 1: Watch Example
I'll use my 'Rip Curl' watch as an example.
Step 2: Watch Back
Look closely at this image. You'll see notches that are cut out of the watch back.
Step 3: Scissor Tips Match to Notches
Now all you need do is insert the scissor tips into two of the notches. Make sure the blades are securely in position before turning the scissors anti-clockwise. The scissors need to be perpendicular to the notches, (not as pictured).
DISCLAIMER: Please be aware that scissors are not the correct tool for this task and in any case this procedure would probably invalidate a warranty. Scissors have sharp cutting blades and the potential for bodily harm and/or scratch damage to the case caused by the incorrect use of scissors is higher than if the scissors are used as intended. Please be very careful. You are warned!
Step 4: Rip Curl Watch Internals
This watch is good to 100m. Here's the internals.
Getting to the battery
Having got thus far you don't want to cause damage getting your battery out. I would recommend using a magnifying glass to figure out how the battery is retained before attempting to remove it.
Closing the watch is just a reversal of this instructable. Have fun and be careful.