I’ve just solved my own question…
If you open the Card widget containing the Notepad Custom Widget, there is an elipse (…) in the top right corner. If you click that, there is an option ‘Open Configuration’.
You can select the theme you would like the Notepad widget to use. Snow is default and shows the toolbar. Bubble hides it.
This setting is on an individual widget-by-widget basis, not system-wide. Simple switch to ther Snow theme when you want to edit using the toolbar, and Bubble when you want to hide it.
This might have been obvious to most, but it was (pleasant) news to me.