I need to send an email to a group of people who don't match any of the search criteria in Families > Email Families. Is there a way to send a mass email to email addresses that have no 'group'?

Run Families > Email Families with as few search criteria selected as needed to produce a list of email addresses that encompasses everyone you need to email. In the Email Preview, uncheck the Check All box to uncheck every email address. Check only the email addresses you want to send to and click Send Email.