The version used for one man's dream is the same on that was released on the tee vee toons cd television's greatest hits black & white classics it's track 23.WALT DISNEY'S WONDERFUL WORLD OF COLOR runs 1min23sec.
hope this helps oh by the way it was written by the sherman brothers but i guess you already knew that ;D
And don't forget that the "Carousel of Color" song was performed on both the TV show and the recordings by the Wellingtons, the trio that sang the "Gilligan's Island" theme on the black & white episodes. Their Disney work predated Gilligan by a few years. They made quite a few singles and LP's for the Disneyland and Buena Vista labels in the early 1960s.