And the North should follow Edmure because? Edmure has no direct ties to the North besides his sister being the Lady of Winterfell. Leaving the North to Edmure would likely cause a civil wat amongst the northern houses.
If he did (very plausible) it could be yet another way to be a thorn in the side of House Stark by an Iron Islander. Davos goes to Skagos, gets killed by the natives, Rickon isn't found by anyone able to verify his identity, and Stannis loses his most trusted advisor to boot. I don't think he lied though, but that still doesn't mean Davosw will succeed. Skagos is allegedly a perilous place.