Can anybody suggest hydrophones for underwater cable-less communication or some other sensor for communicating with a drone for example, under water?
Must be cheep, small and on sound waves. Something like this, but for underwater:
Please define "cheap" and "small" with actual numbers and units.
Transducers for underwater sonar or ultrasound communication are expensive, and require high voltage electronics to drive them.
People have been working for decades on attempts to design and produce an inexpensive, commercial product for underwater communications, so far without success.
That is why you can't buy them "off the shelf". But you might try contacting Fuji, ask them what this system costs and let us know what you learn.