You certainly aren't going to hurt it by cleaning it too much but it isn't absolutely necessary either. I would wipe it off as much as possible, hose it down with some brake clean then install it and fill the diff with the cheapest gear oil I could find then run it in 4WD for a while and change it. I might even mix the gear oil 50/50 with ATF and get it good and warm before I dumped it.
You're really over-thinking it, it's just a diff!
I've got some Yotas, some bikes and a drag car...