I have only given this a moment's thought, but why not just publish the URL map as a text file or SQLLite DB? So at least we know where they went? I don't think it would be a privacy issue since the links are all public?
Making bad actors brute force the key space to find unlisted URLs could be a better scenario for most people.
People also upload unlisted Youtube videos and cloud docs so that they can easily share them with family. It doesn't mean you might as well share content that they thought was private.
How will they know a short link to a random PDF on S3 is potentially sensitive info?