By visiting ip-check.info you may find out if your browser's signature corresponds to that of Tor browser or not. If you use TBB it corresponds to it but if you use another browser it no longer corresponds to it. The idea is to obfuscate this browser signature header using privoxy instead of using Torbutton since if you use privoxy Torbutton no longer obfuscates the signature header. What is the name of that header and how can I replace its value by another value using privoxy?
Even if it were possible to make Tor Browser look like another browser by enabling unsafe features, the list of IP addresses of all Tor exit nodes is publicly available information so it would be trivial to identify you as a Tor user by IP address even without knowing anything about your browser.
I don't know how ip-check.info works in detail, but from testing it looks like it inspects both the browser and IP address. Unmodified Firefox, via Tor gets the message "You are using Tor, but your browser profile differs from the recommended" whereas Tor Browser via Tor gets the message "You are using Tor". So even if you changed the browser fingerprint via Privoxy or otherwise, ip-check.info would still recognize you as using Tor.
So I am afraid there is no way to hide the fact that you are using Tor from services which compare your IP address against the list of Tor exit nodes, like ip-check.info does.