Due to the way the internet works, it is impossible to 'disable' your IP address from others seeing it.
One possible solution is to use an anonymous proxy, such as TOR, an SSH tunnel, or a PHProxy.
The quickest solution would have to a PHProxy. You can find plenty using a quick Google search. Here's an example PHProxy site.
A possibly more 'secure' and anonymous proxy is TOR. Here is what their website has to say about themselves:
Tor protects you by bouncing your communications around a distributed network of relays run by volunteers all around the world
Checkout this Lifehacker snippit for instructions on setting it up
