I don't think so. As best I can muster...Though, they are different I don't recall the Great Escape theme being whistled like the Bridge tune. You might be right.
The song from The Bridge on the River Kwai was not written for the film. So you actually don't even need to suppose that the songs may have been mixed up. The Great Escape theme song was the only one written for the film.
The "Colonel Bogey March" is a British march that was composed in 1914 by Lieutenant F. J. Ricketts (1881–1945) (pen name Kenneth J. Alford), a British Army bandmaster who later became the director of music for the Royal Marines at Plymouth. The march is often whistled.