Water shader with distance fade

Hello,
I'm looking for a way to fade with distance the default WaterProDaytime prefab from the environment pack. I want it to seamlessly transition to the background skybox.
I was able to make a simple surface shader that fades with camera depth with the help of Amplify Shader, in hope I can just copy paste that bit to the Fx/Water shader, but with my zero knowledge of HLSL that turned out to be a little bit more challenging.
An alternate solution might be a fog that takes the color from the same cubemap as the skybox.