Please let me know which version of Hotkeys you're running. Hotkeys' virtual clipboard functionality should not interfere with any clipboard enhancement program (in fact, Hotkeys doesn't do anything to the clipboard until you switch clipboards) since it uses standard Windows calls to communicate with the Clipboard.
The only thing that I can think of where Hotkeys might interfere with ClipMate is being the clipboard owner. It is perfectly legal for multiple programs to be the clipboard owner. It is however possible that ClipMate doesn't like other programs to also become a clipboard owner. If that is the case, try starting ClipMate before you start Hotkeys and see if that solves the problem.