Your AJAX loaded template should have wp_head() and wp_footer(). All of WC templates use get_header('shop') and get_footer('shop') while there's actually no 'header-shop.php' and 'footer-shop.php' files included.
Of course, you could create these two and let 'header-shop.php' be the one-line-of-code PHP page, like so
...and 'footer-shop.php' another file containing only
// all available by WP
...there will be a couple of more inserted by WC.