Two identical sites (with just a logo change) and one WordPress installation

I have two sites I want to setup with one WordPress installation. Both sites will be identical, with the only exception being the logo at the top of the page.

My original idea is to “park” the second domain, and then use PHP to check the domain, and do a simple if/else to set the correct logo.

<?php

if($_SERVER['HTTP_HOST'] == "domain1.com")
	$img = "logo1.jpg";
else
	$img = "logo2.jpg";

?>

The issue I can see coming is using any caching plugin would screw this up.

Is there a better way to do this? I’m not sure I want to delve into WordPress MU just for this…