The nature of URLs is that they aren't secure since anyone can share them. If you'd like to restrict access to a particular person or set of people then you'll need to have some sort of authentication layer, which would be an itch.io account in our case.
You can also try using a password protected page URL, but I'm not sure that's going to give you the security you're looking for. Set the page display mode to restricted, then add a password to the page. You can then link to the page with the password directly in the URL like this:
example.itch.io/mypage?password=MYPASSWORD