With the shortcode [shippingclass] you can display any content on your single product page, which you specify per shipping class within your functions.php. This Snippet includes a fallback which will hop in if the product does not match any (within your function.php file) specified shipping class by you.
I did use it for displaying a free shipping label below the price, if the shipping class is set to free shipping. If the shipping class is not free, the snippet throws out the usual „plus shipping“. This is an enormous powerful snippet, as it allows you to display any content for each shipping class you provide.