When we were developing a new ecomm site with WooCommerce, we needed to adjust Product List Page slightly. We didn’t need a standard ‘Showing … results’ text.
We created a separate file in our ‘functions’ folder (and called it woocommerce.php). This file has all amendments that we apply to default woocommerce behaviour.
Add a reference to this file from your theme’s default function.php:
require_once ( get_stylesheet_directory() . '/functions/woocommerce.php' );
In this file write a following line:
remove_action('woocommerce_before_shop_loop', 'woocommerce_result_count', 20);
As from the code, this removes woocommerce_result_count action from woocommerce_before_shop_loop action which is called before showing your list of products.