Do neither. Assume that he can find Saint Walker's homeworld before he becomes a Lantern. The SI already knows roughly how events will transpire, that Walker's family will all die in his trek to the mountain. What the SI should do is save each family member before they die but trick Walker into believing they are dead just like in the comics. His son gets swept away in a stream? Pick him up when he's out of sight and put a fake body in his place. Someone about to die of malnutrition? Activate a sleeping pill that was implanted beforehand, then heal them after Walker leaves. Stuff like that.
Keep this a secret until after Walker reverts the sun to a normal state, then greet him with his family at the SI's back. This will further solidify Walker's belief that through hope, all will be well.