You can set Link Whisper to insert relative links by going to the settings and activating the “Insert Links as Relative” option. Link Whisper will then create all suggested links as relative links.
This will also enable the URL Changer to change absolute urls into relative ones. The “New URL” in the URL Changer must be a relative url for this to work.
The Auto Link inserted links will be unaffected by this setting, and will insert the links that you specify.