How would a real gentleman say it?
Hexbear argument.
Assuming that you’re referring to “pulling information out of your ass”, you could try: “Pulling facts out of thin air” or “making it up on the go”. Getting more creative with it: “unscripted intellect”, “on the spot expertise”.
Malarkey Nonsense Fabrication
Wingging it.
A real gentleman would probably say “conjecture” or “unfounded information”, but a less explicit word is “nonsense”