In order to save his life from the fate of the previous two captains, it would be sufficient for the captain to refuse to comply to the Ahazya's orders. Going to Eliyahu and begging for his life means that the captain is asking Eliyahu to come with him. However, Eliyahu's agreement to go to the king would seem to give the king the victory as he achieved what he wanted. The Angel commanding Eliyahu to go gives Eliyahu the permission to proceed to Ahazya.

Courtesy of the Virtual Beit Midrash, Yeshivat Har Etzion