I don’t know either how to remove a clip from the source monitor except for replacing it with another clip.
I would usually save (project mlt file, not export/render) and restart Shotcut for this.
You can press File/Close but that will close the project and get rid of the timeline. But the way it sounds, you don’t have anything in your timeline at that moment.
In any case, if the minor changes you have to do externally do not change framerate, resolution and duration of the clip, then you can finish editing your project, save it as an mlt project file and then close Shotcut. You can then replace the files and start the project again.