How certain are you that a displacement sensor will record the wave shape, such that you can measure amplitude? Displacement is not a dynamic variable. You may get a component of the instantaneous wave shape, depending on where you sample the pond water, but you'll also lose some due to flow resistance and inertia.
If I were doing this exercise, I think I'd use the displacement sensor to track long term changes in mean level, and include a low pass fluid filter to intentionally remove the wave signal. Then I'd use a different method, perhaps an opto-electronic method, to measure the wave amplitude.
A fluid filter can be constructed from a small bore resistive tube connecting your pond feed to a vessel, (acting as a capacitor), in which your float is submerged. The filter time constant is proportional to small-bore tube length and horizontal sectional area of the float chamber.
Using LEDs and photodiodes, it is very easy to measure instantaneous wave height to a resolution of 5mm, and with some ingenuity to 1-2mm.
But nothing I've said helps you with the Arduino implementation. :~