How to inject a product field to product display?
I would personally be using views to either override the product page, or I would hide the fields on the manage display page of the product, and show all the fields using a view in a block with a contextual filter to get the content by ID.

However, you can override the product using a template like node--product.tpl.php and use something like...

&lt;?php print render($content['your_field_name']); ?&gt;


To print your chosen field.