I don't think there is any other way. The "Product" post type is referenced all over WooCommerce plugin and its not like you can change the core.
To be honest, post type should ALWAYS have a namespace attached to prevent these things from happening. This includes WooCommerce. They should have named it woo_products or woo-products or something with a namespace. This includes you as well, you should have added a namespace as well from the beginning.