Fyi, here's the text of the letter I've mentioned, from George Zaharias to Fred Corcoran, dated January 29 1951 (on the letter head of the Tampa Golf and Country Club):
"Dear Fred, Received your letter about the Walter Winchell Open, I talked with Babe and she will play in it, she also challenges him to a contest of the manner you spoke of. Best regards to all, and Babe will be there on time."
As mentioned, I think the WW Open is probably the Damon Runyon charity event.
Peter