do_action( 'woocommerce_shipping_method_chosen', 'check_if_dhl', 10, 1 );

function check_if_dhl( $chosen_method ) {
    global $woocommerce;

    $chosen_methods = WC()->session->get( 'chosen_shipping_methods' );
    $chosen_shipping_no_ajax = get_shipping_name_by_id($chosen_methods[0]);

    if (strpos($chosen_shipping_no_ajax, 'DHL') !== false) {
        // 184 is the product ID of the box package
        WC()->cart->add_to_cart( 184 );
    } else {
        // A function I wrote to simplify removing of a product from cart.
        remove_product_from_cart( 184 );
    }
}