Hard-coding a shortcode as the last menu item in primary navigation?

add_filter('wp_nav_menu_items','my_item', 10, 2);
function my_item($items, $args) {
    $items .= '<li class="myclass">whatever</li>';
    return $items;
}

If you have a specific theme location for menu you can target it with :

if( $args->theme_location == 'mylocation' )

EDIT I

you can try

$items .= '<li class="myclass">' . echo do_shortcode('[shopping_cart]') . '</li>';

but it will work only if the function is available.
About the product No. – I have no idea until I see the code that produces it .