Sorry but no. By design, product templates are strictly linked to the product they were created for. Only general templates can be switched between products.
If you really want to "clone" a product template to another product the only way is to import it, change the product while in the designer and then save it as a new product template (this time for the latest selected product).
For this reason, unless there are strong reasons to do otherwise (IE, multisided proudcts or very special setups), I'd always recommend to use general templates instead of product ones.
