What does Sir Gawain offer to do after the Green knight Laughs at their response?

None of the court volunteers as the game seems to imply certain death for whomever plays; the stranger ridicules them all for Camelot's supposed bravery. Eventually Arthur agrees to play the game, but as he is about to wield the great battle-axe, Gawain speaks. In polite and self-effacing language, Gawain begs to take up the boon instead, so the life of the king can be spared in place of a knight as weak and lowly as he.