You have to stop the server and backup your .db and hosting.cfg first. Then delete them from the server. Change the map name (+map Dead_Islands) in the CP startup options, then select "save and restart". It will default to no mods and a vanilla .db, and since the hosting.cfg hasn't loaded the mod for the new map yet, it will default to the islands map.
Then, stop the server and reinstall the original hosting.cfg via FTP, adding the map mod number 1715472692 first in the steam_ugc= line. Restart the server again. It will take some time for the server to download the map and become ready to join. If you run into any trouble, check your server.log to see what went wrong.