There is an option to only remove the Creative Cloud Desktop.
From the main menu go to "3. Creative Cloud & CS6 Products". The first option in the submenu should be the one to remove the Creative Cloud Desktop only.
I recommend contacting chat support if you cannot get it to work. I spent 3 days browsing the forum trying to solve installation issues myself but did not find a solution. After contacting chat support we got it running in half an hour.