WooCommerce – Exclude category from snippet

Since product category is a taxonomy, you could try the is_tax() function. Check for the current category and then manipulate the data:

add_filter( 'woocommerce_get_price_html', 'custom_price_message' );
function custom_price_message( $price ) {
  // Check the current category
  if ( ! is_tax ( 'product_cat', 'category name or id here' ) {
      $price .= ' <span class="price-text">' . __('with shipping').'</span>';
  }
  return $price;
}