Resting wasn't Khan's strong point, but he couldn't ignore Doctor Blackburn's orders. A week wasn't too long in the end, and he only had to refrain from doing particular exercises.
Meditating and relying on the [Blood Vortex] were off the table, and the same went for his time with Martha. Khan was too dangerous in his current state, so he made sure to explain the situation to Cora, Amber, and Martha before booking a training hall for an entire week.
Cora would have understood if Khan requested to have the flat all for himself, especially after their fight. However, Khan believed that Amber or Cora would have still checked on him, and he wanted to avoid that while his mana remained unstable.
Only Headmaster Pitcus knew where Khan spent that week since he had access to the camp's logs. The lack of activities recorded by the training hall also reassured him. It seemed that Khan had really decided to rest, but the truth was far different.