Dhruti, do you definitively know whether or not someone has registered for the event prior to it occurring? If not, unfortunately there isn't much you can do except to exclude those who clicked a link in the first email. Clicking a link would say to me that they either registered, or looked at the page and decided not to register in which case I wouldn't want to send them a second email.
To set the send up the way that you've described above, you could do a flow:
Send [email]
Wait 1 week
Send [email] if not clicked link in email [email]