All you need is to backup the data in the Calibre Library (which is wherever YOU want it to be) and if you feel it's necessary the data in %APPDATA%\Calibre
Both of these can easily be done with any number of tools; take a look at
Allways Sync for instance.
Again; the library goes wherever YOU want. The ONLY stuff on the C drive is the program and the AppData, and if you are THAT concerned about the AppData you should probably use some of the standard Windows tool to relocate your entire home directory to a different; non C drive location.