How do I programatically & DOM (checkout page) remove shipping from a WordPress order if the order contains a specific product type?

I'm trying to do a special logic for my custom plugin. If the user has added a specific product type in their cart, in the checkout page there must be radio inputs that determine whether the user wants the specific product type to be shipped or stored in vault. I've done everything for the frontend part (creating the radio inputs, built the JavaScript logic to remove from the DOM what's not necessary and so on...) but I now need to programatically remove the shipping from the order and remove the "Shipping" row inside the order preview in the checkout page. I tried the following filter

add_filter( 'woocommerce_cart_shipping_method_full_label', 'remove_shipping_labels', 10, 2 );
function remove_shipping_labels( $label, $method ) {
    return '';
}

But it's removing just the label text "Free Shipping" but not the entire shipping row inside the order preview in the checkout page. How can I programatically remove the shipping availability from an order through AJAX and update the user interface inside the checkout page?

function hide_shipping_based_on_prod_type( $rates ) {
    
    	global $woocommerce;
    	$items = $woocommerce->cart->get_cart();
    
    	foreach ( $items as $item => $values ) {
    		$product_id   = $values['data']->get_id();
    		$product_type = WC_Product_Factory::get_product_type( $values['data']->get_id() );
    
    		if ( 'simple' === $product_type ) { //check product types of woocommerce to add more conditions
    			unset( $rates['free_shipping:1'] );
    		}
    	}
    
    	return $rates;
    }
    add_filter( 'woocommerce_package_rates', 'hide_shipping_based_on_prod_type', 100 );

    add_action(
    	'after_setup_theme',
    	function() {
    		WC_Cache_Helper::get_transient_version( 'shipping', true );
    	}
    );