What is a non-vibrating musical instrument?

Answer 1

Strictly speaking, there is no such thing.

Since sound waves are detected by the ear as changes in air pressure caused by vibrations, they must of necessity be generated by vibrations.

All analog instruments produce sounds directly via some sort of vibration.

Only electronic instruments could be remotely considered "non-vibrating." Even then, it's electrical vibrations that originate the signal, and the vibration of the speakers that produce changes in air pressure which the ear detects and the brain translates into sound.