Hello,
Yes, you should copy the file into child theme folder. Don’t change files in parent theme because you’ll lose your changes after theme update.
You may add function to display the post type in child theme functions.php and then use woocommerce hooks in single-product-content.php to show this function. Actually, you may try to do all of this in functions.php of child theme http://prntscr.com/dfnbdn
WooCommerce documentation about this https://docs.woocommerce.com/document/introduction-to-hooks-actions-and-filters/
Regards