I spent some spare time experimenting with trying to move water with a cantilever fan. This is very challenging. Water is roughly 1000 times denser than air, so requires considerable more energy to get it moving. Energy is put into a cantilever fan by accelerating the mass of the fan, so an intuitive starting point for moving water at the same rate as the air fans is to increase the mass of the fan 1000x. Increasing the mass of the fan by this amount is not inconceivable, but it is likely to also dramatically increase the stiffness. This will increase the resonance. In order to have a chance of moving water you really want to reduce the resonant frequency.
I did try stacking a few fans back to back and adding a heavy weight to the end to reduce the resonance. The best I achieved was partially immersing the fans. They would create a lot of splashing, but when fully immersed, they would only have roughly 1cm tip deflection.
Once could conceivably experiment with a stiff/heavy plate and provide the flexibility by attaching coiled torsion springs at the fan root. If one has to resort to bearings, it invalidates a major advantage over the traditional axial propeller.
Fish have achieved propulsion from sinusoidal fin movement, which might point the way to further research.