For anyone who also would like to know how this was done with Debian.
All you have to do it install logwatch and then either remove exim4 and its components or keep them from starting. Once this is complete, you need to change the mailer option within the /etc/logwatch/conf/logwatch.conf to "/path/to/zimbra/sendmail -t" and also add
someuser@yourdomain.com as the MailTo option (you will have to create the conf). Once this is complete you can test it by running 'logwatch' as user root.
You should also add a cron job to run in the wee hours. I have mine set to run at 1AM.
0 1 * * * /path/to/logwatch