First of all, there will be always an IP that's detected. Tor just hides your IP and replaces it with that of the exit-node you're using.
Even though Tor's goal isn't what you're looking for, it's feasible to use it for your purposes, but it might require a bit more work than simply installing the Tor Browser Bundle in order to work consistently:
You either need to configure Tor to give you an exit-node of a certain country via the
ExitNodes command in Tor's configuration file (
torrc), or every time you start your Tor Browser you need to check if the site you want works, and if not, request a new identity until it works.
Setting up Tor is quite easy. You only need to download the Tor Browser Bundle here.