I just clean the housing and brake backing plates etc. The 3rd member should be clean when pulled and stored. If it's not, I use some brake cleaner to rinse any grit and foreign matter out of it before putting it together. Changing the pinion seal if it is seeping is easy to do as well if you have an air tool to zip the nut off. Don't get water on the 3rd member internals.
The rear end will grind most contaminants to dust in a few hundred miles, but its best if there are none to begin with. If you change the gear oil after 1000 miles when warm, you will flush a lot of the any remaining contamination out. I use Dinosaur oil for the first fill and synthetic for the long run. Be sure to add the anti chatter additive if you have a clutch type diff versus the cone type.