draftfile.php links are definitely not going to help you here. They are only accessible to the user who created them and will be deleted automatically after a few days (they are temporary links to be displayed within the text editor in a form, before the form data has been saved and a 'real' link can be generated).
You could try creating a course with guest access and enable automatic guest login for your site: https://docs.moodle.org/en/Guest_access
Once that is done, you could probably create a file (or folder) activity and put the files you want there. In theory, a user would still need to be logged in to access those files, but the login process should automatically allow them in as a guest. This should certainly work for directly clicking on a link to the relevant image, but I'm not sure how well it would work for images embedded in another site.
Ultimately, this isn't really what Moodle is designed for - it's designed for hosting courses and activities, not providing an image storage solution for other sites.