I haven't done that yet, but from what I've seen so far it should take 3 or 5 days on foot assuming that you have no horse yet and that you're following the same rules. Maybe 2.5 days on horseback if you took the left route. I calculated the time to include avoiding Guardians, but if you don't...
From Hateno to Rito Village it is right around 7-9 days on foot or 3.5 days on Horseback. This is assuming that you stop at stables for night, Plan for night so you don't keep going and get stuck traveling at night, and finally you don't travel in rain since the regular NPC's avoid it.
I usually look for cool places to take screenshots, but recently I've been doing a new thing where I figure out distance and time related information. The last one I did estimated that the trek to Zoras Domain from the nearest stable would take you about 1.5-2 days depending on various...