If you're running Active Directory you could push the .msi to your clients via Group Policy. I'm nots ure how safe it is to do with the Zimbra connector, so you may want to test on your own. You can google or search Microsoft's site for the right way to publish applications to computers with Group Policy.
You may be able to write your own scripts to check for an apply new versions as well with msiexec (the tool that performs the installation of .msi files)
may work for you
msiexec /i ZimbraOlkConnector-<version>.msi /quiet