Also, Harry's dark side is "very good at lying." Remember Azkaban? Pretty much every proposition he uttered aloud there was a lie, straight up, and told to pursue a greater goal. If Harry can convincingly pretend, for Bellatrix, to be someone other than who he believes himself to be, convincingly feign innocence and fear when discovered by the auror, and convincingly lie to Minerva about his location, then I think he'd have no problem with this particular deception.

On the other hand, choosing the ring in particular as his hiding target strikes me as somewhat foolish and would require highly conjunctive scenario to be successful. If he has to remain in regular contact with the transfiguration target, though, this may be his best option.