JSON shortcode/export (not logged in)

As somebody who is fairly new to all this, I love your plugin.
I was reading the very last part on this page.

My question is if it is possible to have a page return the json without being logged in. So anyone could do it. If im reading that page right you have to encode everything in the url so also username and password. But is there a way any visitor can do it?

I’m asking because i have a unique identifier and a link in a database. I want to have the search parameter in the url and then return the link in json format based on the request.

I hope it is clear what i mean. I would really appreciate if somebody can tell to me if this is possible.