The link you listed above is the official documentation page, so if it were possible to do this via a URL Scheme call, it should be listed there.
Everything around Day One automation is focused on getting data into Day One. Even their command line utility (which their manual link is broken for), only contains a single command option currently - to create new content. I think the only way to progress this would be to contact the Day One developers (Bloom Built Inc.) and ask if they could add it to their feature list road map.