Are you sure it's the blacksmith's key (name of it just says "Key", but the description when you mouse over it will mention the blacksmith)? Also, where did you end up finding it? Once you have the key, all you have to do is hand it over to the blacksmith by talking to him, then the Trade option will open up.
Alternatively (if you start a new save), you can just do the other blacksmith quest and ignore the key entirely.
EDIT: I was on the Patreon build, so just to make sure, I downloaded and checked for the key on the Free build, too. I found the key in the exact same place as in the screenshot.
