Uh oh, handshaking was complicated because...the image inducer didn't disguise his actual physical self, it was just that: an illusion. Thus, Kurt's demon talons could be felt and most likely regarded as 'not normal.'
However, it would be rude to refuse her handshake, so he did - quickly, and tried not to let it be too obvious that he didn't have normal hands. "It is quite the city," he said, those mutant hands of his going back into his pockets. "I just arrived myself, a few weeks ago. With the people who suddenly arrived too, I think. There have been many new people recently..."
As he spoke, he felt the weirdest sense of deja vu. Did he know this woman? She didn't look familiar...but all the same. It wasn't your run of the mill first meeting, he knew that.
"I'm sorry, I..." He looked down, embarrassed. "I feel like I know you from somewhere." As soon as he said it, he regretted it because, hrmm, yeah, creepy much?