In either case, you could just have your scripts (Javascript/PHP/etc.) echo the stylesheet link into the header based on request or global variables.
Say, in PHP, the code might look like this: (Although I'm a little iffy on PHP URI's, correct me if I'm wrong plx)
Code:
<!-- .... -->
<head>
<link rel="stylesheet" type="text/css" src=<?php
if (isset($_REQUEST['source']) && ($_REQUEST['source'] == "awin")) {
echo("\"styles/alternate.css\");
} else {
echo("\"styles/regular.css\");
}
?> />
<!-- .... -->
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