After having a Jeweller severely scratch my watch trying to get the back off for a battery change, I've been quite paranoid about getting the battery done.
It took me a while to figure out that with a 3D printer I can make my own tools, and being plastic, there's no chance of scratching them, so rather than buying a tool to do it myself, I made a quick design in solidworks and tried it out, and success.
So I have two STL files uploaded, they suit my two watches, one being a casio with a 41mm diameter back, and the other a seiko watch with a 33.2mm diameter back. The actual part diameters are slightly larger.
I added a half inch square drive to use with a ratchet, but I had success with just gripping the outside with my hand. These may also be scaled slightly, but there is a limit as the prongs will get smaller and become too weak and snap off.
So this may not suit everyone, but it's mainly there to show that you can make the tool and swap batteries yourself, with the added advantage of not damaging it at all.
Picture is of initial designs, the STL files are debranded.
I printed on an ultimaker, laying flat.