You might want to look into your specific useage situation, but generally incognito shares the usual information with the server, it only switches off logging to the client.
For instance,in most cases, your wife will not know what you've searched for, but Google will.
Tor is an example of a technology that does what it seems like you're looking for.
There also may be options in your Google settings to opt out of some of their info collection.
Incognito mode has its own ephemeral cookie store, so it serves exactly the purpose he suggested. Yes, that doesn't address the fact that web protocols can still leak quite a bit of identifying information.
Torbutton tries to address information leakage, but it incurs its own costs (e.g. blocking things like HSTS and sharing the entire connection with whoever runs the tor nodes).
For instance,in most cases, your wife will not know what you've searched for, but Google will.
Tor is an example of a technology that does what it seems like you're looking for.
There also may be options in your Google settings to opt out of some of their info collection.