Your best bet is to request a copy of your father's official service record, which would provide a fair degree of detail about his wartime service, including the ships in which he served.
See this page within the Armed Guard website that I manage, http://armed-guard.com/searchmil.html. In particular see section II.A.1 - Records of Individuals, Military, for instructions on requesting a copy of his records. You will have to contact the National Personnel Records Center in St. Louis, MO, and provide as much identifying information as you have (name, date and place of birth, date and place of death, Social Security Number, military ID number ["serial number"], etc.). The page has links to all of the information you will need to request his records, including a required form. There will be a fee for researching, photocopying and mailing the records but the Records Center staff will alert you to the cost before beginning work.
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website