Sorry for the late reply, but if you're still looking for this, you could copy one of the existing files in includes/cron and change it to send your mail (the file name you enter when creating a scheduled task is the name of a php file in includes/cron).
Another way to do it would be to piggy back on the daily cleanup task by writing a plugin for your mail code and using hook cron_script_cleanup_daily.
As for the code, the code that sends the diagnostic email is in admincp/diagnostic.php, in the section that starts with the "Start mail test" comment. That code's written to display any errors that happen when trying to send an email, so it might be more complicated than you need. Or you could copy it and send any errors to yourself in a PM or something like that.
Anyway, I'm sorry I don't have time right now to work out the exact code.
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