Since the game still lacks proper audio options:
To remove the background music, download Snib_NoMusic_P.pak.
To remove the ambient hangar sounds, download Snib_NoAmbientHangarSounds_P.pak.
Place the file(s) you downloaded into this folder:
[YourDreadnoughtInstallationFolder]\DreadGame\DreadGame\Content\Paks
The change takes effect the next time you start the game. To re-enable music or the noises just exit the game delete the respective file again. If they ever add proper audio options you should then also remove the files.
Disclaimer: This is technically a mod of the game, but since no game files actually get modified on disk, you're only adding my files, I didn't see anything in the EULA to disallow or otherwise address this. Nevertheless, use at your own risk.