Normally you would run this on the backend via control panel from your hosting. Cron isn't an Elgg thing, it's a server thing.

You can disable the access level handling within the callback function you register for the cron plugin hook. Then you can access entities during the cronjob execution that would require an admin to be logged in otherwise.

Register in the init function of your plugin:

elgg_register_plugin_hook_handler('cron', 'daily', 'my_cronjob');

and then add the callback function to be executed during the daily cronjob:

function my_cronjob($event, $object_type, $object) {

    $access = elgg_set_ignore_access(true);
    $access_status = access_get_show_hidden_status();
    access_show_hidden_entities(true);

    <now the code that you want to be executed>

    access_show_hidden_entities($access_status);
    elgg_set_ignore_access($access);
}

Just exactly what I needed! Many thanks.