How should the stoppers be cleaned?

Wipe them off with a soapy dish cloth or just a wet paper towel. If you work with glass or something you are comfortable with going in the dishwasher, the stoppers and o-rings are perfectly safe, too. Do not remove the o-rings to clean; nothing can get under them. Also if you do remove them to wash the stopper and the groove is not 100% dry, when you put the o-rings back on, you have just created a micro bacteria incubator!