Solution:
Take a look at the taxonomy-product_cat.php and taxonomy-product_tag.php templates and you will see that they both call the archive-product.php template.
wc_get_template( 'archive-product.php' );
Therefore, if you wish to change the shop archive, but not the taxonomy archives you need to duplicate the archive-product.php to another file… say: archive-product-alt.php and change the taxonomy templates to call this file instead.
wc_get_template( 'archive-product-alt.php' );
Or, alternatively, you could just copy the contents of archive-product.php into taxonomy-product_cat.php.