Even if Conner had been living under a rock and completely clueless on all the things, there was absolutely no way he wouldn't be able to tell that this was Diana. Height aside, she had a power about her that made her seem tall. Almost like Clark did when he donned the cape to fly around and save the world.
He smiled some when Diana hugged Cassie and asked her questions. Politely he waited for his girlfriend to answer before he nodded and took her hand, giving it a firm shake. "Pleasure to meet you Diana," he said, giving her his best and most polite smile (filled with some nerves of course). At the gesture to sit down he unbuttoned his suit jacket and waited for the two women to sit first before he sat as well. These were more manners than he normally displayed but he wanted to make a good first impression.
Even if he wanted to yank off the tie he had around his neck. "I hope we didn't make you wait long."