NiHaoMike
Already buy the enclosure, I'm afraid I can't use another one.
Initially thought to implement the button using capacitive-sensing. But then a tact switch seems to be better:
the microcontroller doesn't have capacitive sense I/O hardware, and will be necessary to wake-up the micro every second to scan the key; also (and more important) there is the possibility of accidental touch detection by splashing water/unintended touch (just by grabbing the thing).
With the tact switch I don't have to wake the micro to read the switch, the switch will wake the micro; and there is no possibility of accidental button activation.
The change in mind is not final, depends on how hard is to do the tact-switch stuff.
BabySitter
It's not for a single-shot home project, but neither for a thousand units product, lets say a few tens per year. Doesn't have to be consumer-grade nice looking quality neither. A few dodginess is allowed

reliability is more important.
I will dismantle some membrane keypad laying around and see if I can use the key-membrane.