Robert A. Iger was grasping for words. Standing before shareholders in San Francisco last month, the normally quick-witted Mr. Iger, chief executive of the Walt Disney Company, had been caught off guard by Brooke Ledwith, an inquisitive 6-year-old. “Who was the first Disney princess to walk on a Disney cruise ship?” she asked, standing on tiptoe to reach a microphone.

As leader of the world’s largest entertainment company, Mr. Iger has command of many facts, but the nautical history of princesses is not one of them. “Tom?” he finally said, as titters rose from the audience. “Can you answer?”

Thomas O. Staggs, who became Disney’s No. 2 executive in February, instantly supplied a satisfying response from his seat in the front row. “We couldn’t choose just one,” he told the girl. “But Cinderella was definitely one.”

For 25 years, Mr. Staggs has devoted himself to the Disney brand, whether closing the $7.4 billion purchase of Pixar in 2006 as chief financial officer, or christening Walt Disney World’s Seven Dwarfs Mine Train last year as theme park chairman. (Yes, Snow White was there too.)