Yeah I'd shake his hands. I'm used to all sorts of people coming through so I'm used to this kind of thing by now, though I'll admit I've never encountered this specific species before. Working at an intergalactic ship port, even in a remote place like Earth, will desensitize you to a lot of stuff.
"Welcome to Earth, traveler."
I stick out my hand to shake his.
"And now I don't mean to be speciesist, but don't you go 'round causing trouble. Otherwise, enjoy your stay."