You can wash the first Oura ring with water with a mild soap if needed – basically, anything that's safe to use to wash your hands should be safe to use to clean the ring. Rinse and dry the ring carefully, and make sure that no soap residue is left on the inside.
To ensure good contact with the charger, it's good to clean the gold coated charging contacts inside the ring every now and then using e.g. a Q-tip or a soft tooth brush.
Occasionally you may get stains/black marks on the Arctic White ring. In case this happens, you can use a magic eraser or a pumice stone to remove them. Stains on the Stealth Black ring can be cleaned carefully with a magic eraser sponge.