The better way is to remove axles. Take the inner axle off with the Ujoint. Replace the outer stub axle and bearing. remove the Drive line. Now you have 2x4 that can roll.
You have to remove the axles anyway to get to the carrier. So just stop at the axles. Plug the outer housing with a rag, rap in a plastic bag.
Thats for the front.
The rear well if you can drive it but the more you drive it the worse it gets. I could see taking the ring out if I had to go along way. But it is amessy job out on a trail and some places you better?should anyway. have a spill kit.