All you need to do is move Cookie.app to the trash. if you want to do a clean install, also delete:
~/Library Application Support/Cookie (favourites)
~/Library/Prefences/com.sweetpproductions.Cookie.plist (settings)
*you will lose all your settings, and favourites if you remove these two files.
you will then be able to open the App Store, login, and re-download from the "Purchases" tab.