Detecting the amplitude of waves on water

At this stage I don't know how linear the wave height/wind speed relationship is going to be at the mm scale.

Have you tried looking it up? The relationship seems to have been studied for pretty extensively, especially for wave amplitudes < 0.1 m (capillary waves) which can easily be generated in the lab. Google pulls up a bunch of examples -- a couple of random selections:
http://www.ifm.zmaw.de/research/remote-sensing-assimilation/research-in-the-lab/bound-and-free-gravity-capillary-waves/

If you want to repeat the work, obviously you will have to directly measure the wind velocity anyway. Much easier to measure than water wave amplitude.

A chemistry professor I know says he often reminds his students that "two weeks in the lab can save you an hour in the library".