He has visited at least 80 countries, and when John Peterman says “visited,” he means it. “That’s not just stopping at the airport to change planes,” said the founder of J. Peterman Co., the clothing company that’s acquired cult status due to its hand-illustrated catalog and fancifully narrative product descriptions that often reference far-flung places. At 77, Mr. Peterman still regularly sets off from his Lexington, Ky., home to destinations like Paris and Buenos Aires. “I’m going out and looking for inspiration,” he explained. He insists that if you want to find the proper cut of a kilt, you must tramp around Scotland...