I'm not sure that you can. The nonces were introduced to prevent exactly that sort of thing (somebody creating external links and tricking users into clicking them, thus causing those actions to occur).
A delete link looks like this:
Anyway, the whole point of nonces is to make sure that all WordPress actions like this happen from the wp-admin screens. Now, if you knew the nonce, you could pull that link and thus do a delete (assuming you also sent the proper cookies to do the user authentication). But the nonce changes every 12 hours for every link in the wp-admin screen, and is only valid for 24 hours after that.
More info here: http://markjaquith.wordpress.com/2006/06/02/wordpress-203-nonces/
Note that all the AJAX is really irrelevant. If you get the right URLs with the right parameters, the relevant actions happen. The AJAX just makes it pretty. But with nonces, you'd have a lot of work cut out for you to duplicate that logic.