What do you mean by receiving attributes from a URL? Do you mean query parameters? Or are you asking if there is a way to combine the fetching of the document via the URL and the extraction of JSON fields from the response? If the latter, there isn't a way to combine those currently; NiFi is a highly modular system so fetching is really a different operation than extractions, hence the two separate processors.
What do you see as the issue in receiving the whole JSON response? The third-party libraries I'm familiar with still retrieve the whole HTTP response whether they expose it via an input stream or a big string or whatever.
After the initial fetch/response, if you don't touch the content after that, there won't be an operational impact with the respect to the size of the JSON response. If you no longer need the content, you can replace it with something else (or nothing) using ReplaceText.
One concept that is (hopefully) becoming more popular with web services is support for GraphQL. Using that paradigm and query language, you could ask for just the fields/structures you want, and you get the response you expect.