Can the note size be changed independent of the staff size?
Currently there isn’t a lot of options available for changing a notehead size, but if you select a note (or group of notes) and right-click, in the pop-down menu there’s a “Notehead” section. In there you can choose from a variety of notehead styles. Since you’re specifically asking about size, you’ll note that there’s “default noteheads” and also “default noteheads (large)” which does about what you’d expect.
If you want something smaller I’m afraid you’ll have to use a none-regular notehead, but the “old-style diamond noteheads” option is useful in a pinch for something smaller that doesn’t look too foreign.
There is at the moment no way to make notes cue-size, though.