Hi there,
It is possible that shop_order appears as a Post Type because our plugin essentially picks up all post types, without discrimination, that are available in the WP instance. It was primarily designed so our customers could pick and select any custom post type that they wanted to enable push notifications for. It is probably not the best solution and we will consider changing the drop down to not show ALL available post types. Your suggestions are welcome here.
Our engineering efforts are primarily focused on making the existing set of features robust and scalable and support for WooCommerce is not in the pipeline at this time.
Hope this helps. Feel free to ask any follow-up question(s).