Clarification: The “app” doesn’t actually matter, because it’s connected to where you’re importing to, not which blog or user that you’re importing from.
When you create an app on Tumblr, you put in a “Default Callback URL”. That URL has to match where you’re running the importer. The app is connected to that specific place. It’s used for authorization.
But what “blogs” you see as being available to import isn’t connected to the app at all, it’s connected to who you log into Tumblr as. If you get the username/password of a different user and connect as them, using the same app you already made, then you’d see their blogs and be able to import those instead.
So leave the app alone, and put the same key and secret back in. But then, when you do the authorization step, login as the user who has access to the blog you need to import. Then you’ll see their blogs and can import them.