My question is: Is it possible to write a script which allows to access different features (like video mode, zoom in/out, ...) just by different combinations of these two buttons?
Sort of.
CHDK release 1.3.0 lets you monitor the status of the shutter button and take action in your script based on its status. Prior versions of CHDK don't allow that - the shutter button is only for starting and stopping scripts when CHDK is in <ALT> mode.
There is currently nothing similar for utilizing the power button unfortunately. AFAIK, the button starts the camera electronically but stops the camera through software (i.e. the Canon firmware monitors the button state and shuts things down gracefully if it's pressed.) So it should be quite possible to also "trap" the power button with CHDK and allow a script to monitor its state and take action (including camera shutdown if desired). I think it's a case of nobody having a need for this behind why it has not been implemented yet.
The idea is to first activate the script before putting the camera into the underwater case.
That would be hard on the battery life and not necessary. You could still start the camera with the power button once underwater. If CHDK is installed on the SD card, it can be configured to automatically activate the script at start-up. You could even initiate a button sequence to power the camera off when you are done.
Still, trying to do funky button press sequences underwater might be a frustrating experience. But that's up to you relative to the cost of a better enclosure.