Zuko doesn't notice the weapon he's trying to keep within reach, though even if she did, he hardly seems like any kind of threat in the condition he's in. She doesn't make any effort to look friendly herself--maybe that's something she should work on, but it just doesn't occur to her. At the least there's nothing threatening about her body language. She crouches down not far in front of him, trying to look him over.

"I don't think you need to be worried about manners right now," she states flatly. "How badly are you injured?"

He clearly doesn't have a grasp of his situation yet, so it's hard to tell if his casual remarks are just part of his usual personality or if he's suffering from some kind of head injury. If he can't move enough to walk even with support, then she might have to go back to the Bastion for help.