Okaaaay - let's invent a new one then.
Use three small transducers mounted in a straight line fore-and-aft. Emit pulses of sound from the centre transducer and receive them on the forward and aft ones. Measure the time difference. Compute speed.
Of course noise will be a nuisance, but by using spread spectrum sound and suitable processing this would not be a problem.
Would it attract any attention? Nope, not here. Nobody understood the ion anemometer I posted on page two and I guess nobody will understand this one, apart from Gums who will recognise it as a use of doppler.
Retires all bitter and twisted to kitchen/workshop. Hat, coat, soldering iron....