I use a this line of code in my sites in order to change my header (and hence my css) depending on what template I'm using:
<?php include ('otherHeader.php'); ?>
however, with woocommerce that doesn't appear to be an option for shops. My client has asked specifically that I separate his products onto two separate shop pages, which look different. I've already managed to separate the store into two pages through the menu using product categories instead of the shop page, but is there some sort of code I can insert into my archive-product.php file so that it will check which page it's on, and choose it's header accordingly?