Water molecules, as many people know, are polarized, and so water molecules tend to have an attractive force between them. But how would the waves in water behave if this attraction no longer was present, but everything else was the same?
There are different factors that make water a media for waves. For transversal waves the viscosity and cohesion of molecules are essential. Even if the water is assumed not to evaporate. Try to imagine pushing a boat forward in a liquid with low viscosity. The propeller will just easily skid without generating any wave or traction.
However for P waves a liquid with low or no viscosity would still work as long as it can contract and expand under stress. If you in a crude way look at a differential cube of that liquid omega= (k/m)^1/2. K is the water stiffness index and m is its mass.