Of course I guess the part wasn't easily available... ;-)
2 solutions (which need to fully disassemble the camera. Thanks to ifixit for that)
First solution - locate the top plate circuitry (where is the faultive on/off switch) and solder carefully a very fine wire between the two terminals to make a short circuit and permanently set the state of the camera "ON".
Reassemble the camera, put a battery in it.
The camera turns on automatically and stays ON. (if it doesn't press the shutter button)
The camera goes automatically OFF after few minutes if you don't take photos.
To wake it, just press the shutter button few seconds.
It could be the best solution.
Second solution, slightly different : if you have a stock of electronic parts and have the chance to find a very tiny on/off switch, connect it (solder...) on the two terminals of the broken switch. With 2 long and very fine cables, you can easily have an "external" switch (for exemple on the bottom plate).
This is what I did.
It works fine. Not very elegant, but at least the camera is not in the recycle bin and is still working.