I don’t know enough about clipboard switcher, either, but I saw that you hadn’t received a reply yet, so here goes. Some apps have proprietary clipboards that aren’t compatible with KM’s clipboard history.
For example, I sometimes use MPEG Streamclip to edit video, and I can cut copy and paste away inside a video window in the application, but the clipboard history of KM won’t change and can’t be used in other contexts.
One way to test (KB 8) is to create a new macro with a trigger something like “when KM deactivates” with the single action Activate clipboard history switcher. Then when you’re ready to check, you can launch KM, then click the desktop or something to show the history. Copy some different stuff, then open history again (by activating KM and clicking the desktop) to see if the contents changed. After you’ve made your determination, you probably want to clear clip history and disable the macro.