Update the Woocommerce No Shipping message to include contact details.

woo-no-shipping-available-message.php

add_filter( 'woocommerce_cart_no_shipping_available_html', 'myplugin_no_shipping_available_message' );
add_filter( 'woocommerce_no_shipping_available_html', 'myplugin_no_shipping_available_message' );
/**
 * Update the Woocommerce No Shipping message to include contact details.
 */
function myplugin_no_shipping_available_message( $message ) {

	$country = WC()->customer->get_shipping_country();
	$mailto  = 'mailto:' . get_option( 'admin_email' ); // Could also be 'woocommerce_stock_email_recipient'.
	$link    = sprintf( wp_kses( __( '<a href="%s">contact us</a>', 'my-plugin' ), array( 'a' => array( 'href' => array() ) ) ), esc_url( $mailto ) );

	if ( ! empty( $country ) ) {
		$all_countries = WC()->countries->get_countries();

		return sprintf( 'Please %1$s for shipping rates to %2$s.', $link, $all_countries[ $country ] );
	}

	return sprintf( 'Sorry, no shipping options were found. Please %s for shipping rates', $link );
}