Unfortunately there were a number of ships during World War II that had "Walker" as part of their name so I cannot pinpoint the ship in which you are interested.
There were at least seven ships in which Walker was the last name (Elisha Walker, Francis Amasa Walker, John Walker, Mary Walker, General Nelson M. Walker, Robert J. Walker, Samuel H. Walker) and two ships with Walker as a first name (Walker D. Hines, Walker Taylor). Finally there was also a U.S. Navy destroyer, USS Walker, DD-517.
Of the above, most can be eliminated as likely candidates based on the name and/or construction date. (For example the two ships with Walker as a first name probably would have been referred to by their last name, not their first name.) Likewise the destroy would not have been referred to as "SS" Walker. Several ships were built in early to late 1943 or later, so do not fit your timeframe.
Two ships best meet your description: Elisha Walker (a tanker built in 1920) and John Walker (a cargo ship built in June-July 1942).
Can you supply any more information, such as the full name of your grandfather and his birth year? I may be able to find information using his name and correlate that to the name of a ship. Also, keep in mind that Armed Guard sailors often served in more than one ship, so you may be interested in more than "SS Walker."
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website