From page 12 of the KeyForge rulebook(bolding my own, linked below):
When a creature with the skirmish keyword is used to fight, it takes no
damage from the opposing creature when the damage from the fight
This applies only to damage that would be dealt by the opposing
creature’s power, not by damage that is dealt by keywords or other
Thus the creature with Hazardous does damage to the Skirmish creature before the fight resolves per the wording of Hazardous (clarified in the rules as, "When a creature with the hazardous X keyword is attacked, it deals X damage to the attacking creature before the fight resolves."