In Pretty Links, set your redirect type to Meta Refresh or Javascript to replace the original referrer with the pretty link URL. See Understanding Redirect Types for details.
So if the link was embedded on a page like https://www.coolforums.com/topic1/thread0/, the referrer would not be shown as that URL, but as the Pretty Link URL (http://yoursite.com/xyz) instead.
To further wipe out the referrer, add this to the scripts section of your link, or to the global scripts section:
<meta name="referrer" content="no-referrer" />Most modern browsers support that and will not pass along the referrer at all.
If you continue to have issues with this, please send us a support ticket.