That's not exactly correct. narita re-screens transit passengers but does not clear them through immigration.

Also, if your bag makes it to Narita, you can bet it will make its connection. Narita rarely misplaces bags on any of the carriers. Be aware that connecting DL to CX you will change terminals however.

Even if you are not on a single ticket, the agent shouldn't have any trouble tagging your bag all the way through.