Wow! WE did this recently and had no line at all! I asked about an appointment in the morning on our way to the Crystal Palace. The barber said to return during the parade for the shortest line. It just happened that we did indeed, return just before the start of the parade. There was no line at all!
What was better, was that we came out just as the parade was starting. We're normally not big parade people, and my daughter isn't a big hat person (or rather, wasn't), but we finished just as Mickey was coming by. At first my daughter was trying to get her ears off, but then Mickey pointed to her in the crowd (he was pointing to all the kids w/ Mickey ears)! As little as she is, she squealed with joy, and delighted in watching the rest of the parade from her perch on Dad's shoulders - clapping and wearing her Mickey ears the whole time. It was dad's favorite part of the trip.
After the parade, the ears came off. But now that we are home again, she enjoys wearing them sideways.