You do not need to do anything to the server to change Oasis, just activate the other in myrealm and it will push it to the new server.
It is NOT akin to burning. While your walkers will move to the new oasis, your structures etc. will stay on the old one. When you switch back, they will still be there. However, High Quality materials only mature on active servers, so keep that in mind when switching.
You cannot delete or change oasis in any way. That's on Donkey Crew to add (and lord knows we've told them in the discord it's needed).