You should try uninstalling the apps first.
If that doesn't work then yes, delete or rename the .desktop file, but it's in share/applications, only the icon is in pixmaps.
The only problems with that is that you will have to know which of the duplicate ones you want to keep and which one you want to delete, and that the app will still be taking up space on your system, unless you can locate all it's files/folders and delete them too.
Option 3: Start again with a clean image.