Transients expire on their own. No need to unset them.
And to call wp-cron manually is simple. Just define DISABLE_WP_CRON to true in the wp-config file to disable the normal cron spawning process. Then make your cron system hit wp-cron.php manually every so often to process pending jobs.
There is no other special trick that you need to do. No need to fool around with transients or special coding.