Sorry, I had my post deleted before you replied. The ["0"]
I suggested as a default, effectively pre-selects that (None) option.
It wasn't a valid answer to your question Andy so I got it scraped.
For your use case, you should probably use a Named Template as the Edit Format, and input the name of your custom template in the Format Parameters. (search templates named like option_template_* for some examples).
I'm not sure if the 'widget_def_options_new_posts' template could work out of the box as an option template.