ClickDimensions allows use of custom CNAMEs as described here but if you are looking to combine your CNAMEs with secure URLs for Emails (those beginning with HTTPS), please review the information below.
URLs within ClickDimensions emails can only be used with HTTPS as long as the default CNAME (elink[eu].clickdimensions.com) is used. This is because, at this time, we do not have the capability to hold a security certificate for a customer’s domain to enable HTTPS used with a custom email CNAME (link.yourcompany.com).
In order to work around this, you can remove the custom email CNAME. Any email that uses the default email CNAME, will also use HTTPS for URLs within the email.