Hi findezel1,
There will not be any issues, while you are installing the Adobe CS6 Design Standard, you would not have an option to install Adobe Photoshop CS6 as its already installed.
Alternatively, You may de activate and uninstall the Adobe Photoshop CS6(curently installed) and keep it as a back up and use the Photoshop which is a part of Adobe CS6 Design Standard.
^Ani