The earliest known citation I know of for ‘the whole nine yards’ is from 1907, which disproves any WWI or II origin. From The Mitchell Commercial (an Indiana newspaper) 2 May 1907:
“This afternoon at 2:30 will be called one of the baseball games that will be worth going a long way to see. The regular nine is going to play the business men as many innings as they can stand, but we can not promise the full nine yards.”
The same paper a year later, 4 June 1908:
...Roscoe went fishing and has a big story to tell, but we refuse to stand while he unloads. He will catch some unsuspecting individual some of these days and give him the whole nine yards.