In non-wartimes, it was common for US Navy vessels to insert their location in the killer bars. Many, many US ships were in Tokyo Bay in the weeks after the end of the war. While some of the mail would be "philatelic", much of it would be carrying real "live mail" back home to family and friends - the killer being merely a bonus.
Here is an example from the USS Ticonderoga, which did not get to Tokyo Bay until Sept 6 (too late for the ceremony on the USS Missouri), and mailed several days after arrival. It contains a small Japanese flag.
It is certainly authentic, but identifying which ship the original poster's "Tokyo Bay" killer came from is a challenge and the exact date certainly unprovable. It does not match lot 514 in the auction link above, but does broadly demonstrate the creativity of postal clerks to make-do during their ship's visit to the Bay.