Keep in mind that this is over simplified so any conclusion based on this is not trustable. It is just a rephrase of your idea, which I don't agree.

The wave is f(x,t)=A*sin(k*x-w*t).

At any moment the ship stay parallel to the water surface, which is described by tan(theta)=df/dx

Once you define the theta carefully you can write theta=atan(df/dx).

The angular velocity is then d(theta)/dt.