Little shit
The ship's passenger area had no scanners or screens that could reveal its route, and that aspect was intentional. Everything about Colonel Norrett's evolution had to remain a secret, even during the last hours before the event.
As for Khan and Headmistress Holwen, their conversation ended after those few lines. Khan had more questions, but any answer would only intensify his curiosity. It was better to wait and experience the real deal with the entirety of his senses.
The lack of distractions inside the ship made the trip quite boring, especially since it stretched for hours. Neither Khan nor the Headmistress knew how long it would take to reach the intended destination either, which worsened that dull wait.