Replace SuperSide Me's default search input with the WooCommerce search.

functions.php

<?php

add_filter( 'supersideme_search_output', 'prefix_use_woo_search' );
/**
 * Replace the default SuperSide Me search form with the WooCommerce product search.
 * @param $search_form string
 *
 * @return string
 */
function prefix_use_woo_search( $search_form ) {
	if ( function_exists( 'get_product_search_form' ) ) {
		$search_form  = '<div class="search-me">';
		$search_form .= get_product_search_form( false );
		$search_form .= '</div>';
	}
	return $search_form;
}