how to use different page design for different category

For overriding default templates please check this.

If you want different/custom category template for specific category then you may create a php file which has naming structure like taxonomy-product_cat-{slug}.php. For example, to create custom category template for clothing category, you will need to create taxonomy-product_cat-clothing.php where clothing is slug of the category. Place this file in the woocommerce folder of your theme where you may have overridden other WooCommerce templates. I hope this helps.