My suggestion is to...
1. Create a new file with a random file name in your /admin directory.
2. Paste in the contents of the admin_delete_stories.php file.
3. Remove lines 11-23 (pasted below)
Code:
check_referrer();
// require user to log in
force_authentication();
// restrict access to god only
$canIhaveAccess = 0;
$canIhaveAccess = $canIhaveAccess + checklevel('god');
if($canIhaveAccess == 0){
header("Location: " . getmyurl('login', $_SERVER['REQUEST_URI']));
die();
} 4. Save the file and you should now be able to run it with a cron job.
I haven't tried it myself, but I think those are the lines that make you authenticate as an admin user in order to run the file.