You can force WooCommerce to only show free shipping rates if the carts contents qualify and hide the other shipping rates with this code snippet below, which uses the woocommerce_package_rates filter, it goes in your themes functions.php file
add_filter( 'woocommerce_package_rates', 'prefix_hide_shipping_when_free_is_available', 100 );
/**
* Hide shipping rates when free shipping is available.
* Updated to support WooCommerce 2.6 Shipping Zones.
*
* @param array $rates Array of rates found for the package.
* @return array
*/
function prefix_hide_shipping_when_free_is_available( $rates ) {
$free = array();
foreach ( $rates as $rate_id => $rate ) {
if ( 'free_shipping' === $rate->method_id ) {
$free[ $rate_id ] = $rate;
break;
}
}
return ! empty( $free ) ? $free : $rates;
}
