It's a single press, which has to power the microphone for several seconds, and wireless connection to communicate with the sync device, even later if it isn't immediately available. In what way would piezo generate that much energy?
I see. However that misses the point of always having the function at hand, 24/7/365. There will be the off time when you remove the watch to charge it for instance, or times when it may be inconvenient to wear a watch.
Your use case would be another product, likely with a different audience.