One fix is to not directly send the users to the result page. Instead link to a redirect script on the ddg servers i.e, duckduckgo.com/goto.php?link=http://search-result.com/ and then have goto.php remove the REFERER from the request headers.
<?php
header("Location: the-result.com");
header("Referer: ");
?>So maybe you should have tested it ;) ?