This one took me a while to find, but it’s fairly simple when you find the right filter for the job. Luckily WooCommerce has filters and hooks for almost any need.
Place the following snippet in your functions.php and the notice about shipping options being updated should be gone
add_filter( 'woocommerce_shipping_estimate_html','__return_null');
Let me know if it works for you, or post your questions in the comments
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