The anchor sound for shipyards is much louder than other sounds, especially the unanchor sound. There have been complaints about this for years, but the sound is still the same. I have finally found a way to "fix" this.
I found a file that defines what sounds to use for some of the sounds. The anchor sound is in the file. There are other sounds listed for other situations, so I experimented with different sounds until I found one that is quieter and seems like a reasonable sound for anchoring a shipyard.
I made a mod that changes the sound to the quieter one. I don't know if it works in existing games or not. It's worth trying if you have a game going. It works in new games. I use it all the time.
You can get the mod here.