Hiya olphil,
You could make a change to your WA_Universal_Email/WAUE_contact_1.php file.
Find the line:
$MailFrom = "".((isset($_POST["Email_address"]))?$_POST["Email_address"]:"") ."";
And change it between the quote marks to anything@mydomain-name.com (the first bit can be anything, the mydomain-name.com is obviously the name of the domain you're sending from. So an example of the whole line is:
$MailFrom = "web@mydomain-name.com";