Bring a long drinking straw with you, and pair of goggles or snorkling face mask. After it gets dark, sneak into the Jungle Cruise or River of America (?), get into the water, and use the straw to breath with until after closing.
Of course, you shoudl ride JC, or the Liberty Belle Riverboat to scout out a good place to hide.
Another option would be to ride the WDW Railroad to scout out a place to sneak into the woods from Frontierland. Or you could just jump off the train somewhere behind Fantasyland but before Toontown.
A third option would be to try and find out the secret code to the missle control room door behind the secret panel in the Castle. If you know the code, a door opens, which leads you down a set of steps to the missle control room.