You use either the "the" or no article, but it's such an odd thing to say. Have you already discussed what happens when it's used inappropriately?
This product, when used appropriately, will... may be a better choice for you, depending on context.
(The use of "an" suggests there are at least two ways to appropriately use the product, and this one way will do something, while another way will do something else. This seems unlikely, but even if you wanted to say that, "one" would be better than "an.")