You can't hide your IP address from the proxy, but assuming the proxy is not passing it along in an X-Forwarded-For or similar header, your browser will not pass the IP address along in the HTTP request (and never in the User Agent). You do need to disable all 3rd-party plugins and prevent cookies from being passed as they may separately reveal the IP address.

This page will display the proxy headers which might be passing your IP, but more likely it's flash or java or something else sending it: http://my-addr.com/ip