His offer not to touch her puts her at ease. It's nice for a man not to assume, for once, to actually put some thought into what she might or might not want or be comfortable with.

"It's fine. Thank you." She reaches out for his arm, closing her hand gently around his wrist. "Sitting down might be best. This is all just a bit much right now." Being sick, being on a cruise ship, being forced on.