"Not long, no," he tells her and yes, he does consider propriety in how they walk, not holding her too close. But would he not seem rude to walk apart from her?

This is what he tells himself. "A week, perhaps, at most." The days here, with so little to do, tend to blend together. That was his thought, anyway, before he saw her. "Have you been here long, your Highness?"

See? They are merely walking, merely making conversation. Nothing to see here.