Klaus wasn't scared of the young man, he knew he wouldn't want to die, so why should he be afraid of his threats?
While they were fighting, he had secretly communicated with Grey, he would create an opportunity and Grey would unleash his ice domain. He would also use his personal domain with it as well and also send out a powerful ice attack with his sword. With all these, the possibility of the young man not freezing to death was low.
Grey had agreed to it without a second thought, if they could take this person out, it wouldn't be a bad thing.
….
On Grey's side, although he was not pressured, he was a little taken aback when Klaus suggested their joint attack. He had seen a glance of Klaus using the sword and knew that it was a great weapon. It was most likely something he obtained here since he didn't know of it.