So my guess is that Daddy carried this picture with him during World War II and it was handy when he had the opportunity to get Dempsey's signature on the ship.
This paragraph from the Wikipedia article on Dempsey actually mentions his serving on the USS Wakefield: Wikipedia on Jack Dempsey
When the United States entered World War II, Dempsey had an opportunity to refute any remaining criticism of his war record of two decades earlier. Dempsey joined the New York State Guard and was given a commission as a first lieutenant. Dempsey resigned that commission to accept a commission as a lieutenant in the Coast Guard Reserve. Dempsey reported for active duty in June 1942 at Coast Guard Training Station, Manhattan Beach, Brooklyn, New York, where he was assigned as "Director of Physical Education." Dempsey also made many personal appearances at fights, camps, hospitals and War Bond drives. Dempsey was promoted to lieutenant commander in December 1942 and commander in March 1944. In 1944, Dempsey was assigned to the transport USS Wakefield (AP-
21). In 1945, Dempsey was on the attack transport USS Arthur Middleton (APA-25) for the invasion of Okinawa. Dempsey also spent time aboard theUSS General William Mitchell (AP-114), where he spent time showing the crew sparring techniques. Dempsey was released from active duty in September 1945 and was given an honorable discharge from the Coast Guard Reserve in 1952.