I can assure you , Your information is 100% backwards
Think of an ip address being similar to a street address.. How would you hide that. By sending without a street address right?? Well in tcp/ip land this cannot be done as packets need a source and a destination address in the header of the packet for communication to be possible. Now source addresses can be forged, but for communications to come back to you , the real address of your box is still in the packet headers.
You can use a web proxy , but they log what IP connected to it and what that ip requested at what time. So the web proxy would have the information that you're thinking is "hidden"