Hi Gerry!
I wasn't going to attempt answering this question, I thought it wouldn't be of interest to me, well I'm pleased to say I took a second look and thought I'II respect you wishes not to use google or wiki so I asked Jeeves instead (I needed to now exactly what's what before I offered an opinion)
I found out more about the "Kilroy was here" slogan and I thought whilst I was reading, is this just an accident, and sure enough a theory that to me sounds the most plausable.
James J. Kilroy, an American shipyard inspector. During World War II, Kilroy worked at the Fore River Shipyard in Quincy, Massachusetts. It was there, he claimed, that he used the phrase to mark rivets he had checked. Kilroy counted the rivets installed by workers who were paid by the rivet. At a shift’s end, a riveter would make a chalk mark to show where he had left off. The next riveter started at his mark. Dishonest riveters discovered that, if they started work before the inspector arrived, they could make more money by erasing the previous worker’s chalk mark and chalking a mark farther back on the same seam. They took credit for some of the previous riveter’s work. J.J. Kilroy stopped this practice by writing “Kilroy was here” at the site of each chalk mark.
Back then, ships were sent out before being painted, so when sealed areas were opened for maintenance, soldiers found “Kilroy was here” scrawled on the metal. Thousands of servicemen may have seen his slogan on the outgoing ships. This Kilroy seemed to be everywhere, thus starting the legend.
The theory holds that servicemen began placing the slogan on different places, especially in captured territory and landings. At some point, the snoop-nosed drawing emerged to accompany the slogan.