The API is already made and can be found at https://github.com/julien040/hn-recommendation-api. I don't think it would be too difficult to build a Chrome extension that fetches it.
You can use the app itself to make some surprisingly powerful shortcuts, and then share them in some kind of text based serialized form (don't remember the details). I'm sure there are also ways to make them programmatically, but I doubt it would be necessary for this use case.
Seems like you basically want to extract the URL of the HN page, store it in a variable and then append that variable to the URL of your recommendation engine. There are probably more fancy variants of "extract text" that you could use, too - I'm not sure of the details.
For now, it only pushes the shared URL to the recommendation engine. If I have more time, I'll try to find a way to extract the URL from the HN page.