Here is Daniel Wexler's response to my email to him requesting information:
"I had no recollection of a course located on the JFK site and, at least so far as prewar sources go (e.g. American Annual Golf Guide, Golfer's Yearbook and others) I find no record of one. That said, it clearly did exist by 1942 as several internet sources indicate the city buying it out prior to constructing the airport. As my 1939 Federal Writer's Guide to NYC (whose maps were reasonably thorough where golf courses are concerned) shows nothing even in the immediate vicinity, I wonder if it was actually an open, completed facility or maybe something under construction or, at any rate, very new. The likelihood that it was anything notable is, I'd expect, extremely low."