Links fire GET requests by default. You cannot fire HTTP GET requests without passing parameters through the URL. The only what can do this is HTTP POST. All parameters are then included in the request body. But you would need to replace all links by forms with buttons and you need to modify the server side code so that it listens on POST requests instead of GET requests to take actions accordingly.
Javascript can also fire GET requests just in "the background" with help of XMLHttpRequest, but when a client has JS disabled, your application will either break or still display the parameters. Also the client has full control over JS code, so it does not necessarily "hide" the parameters from the client, but only from the browser address bar.