I'm sure I'm not the only one that notices that the silver spartan's armor configuration/design shares much resemblance with the spartan IV configuration/design. I think it's fairly safe to speculate that the spartan is a spartan IV. That, along with Noble six's death scene, can most likely rule out the possibility that Noble six is the hidden silver spartan.
Additionally, I believe John is in fact looking for Mendicant Bias. Clearly, the design of human AI's is very similar to the design of forerunner ancillas. (I, for one, believe this is no coincidence, especially considering the librarian's impact on humanity). With that in mind, I think John may also know that. In his knowledge, he may believe that he can transfer Mendicant Bias onto Cortana's chip. Keeping it to himself, perhaps, so no one else may have access to it.