Three masked men burst into the room, ordering people face down and asking who was from America. One put a black hood over Andres Gonzalez’s head and lined him up with other hostages. He got short of breath and knew his legs were shaking—even though he also knew this was only classroom training and the guns were fake.

Mr. Gonzales, a Hyatt hotel executive from Miami who travels frequently, was learning how to spot travel trouble and respond to dangers, from terrorism attacks to kidnappings, pickpockets and scammers preying...