if you are only allowed to have a self powered unit, then lowest power use makes the most sense as does battery voltage monitoring.
a mechanical switch could power your device, and it would start, test power, send the message.
then time-out and shut off power. at that point, there is no power used.
If it will be powered on all the time, then the battery life will be less
it would seem that a simple way to change the battery will be key to make this project easy to use.