Put it in the dishwasher. Let it dry. Spray button with "Tuner Cleaner" from radio shack or some 3M contact spray. Keep it away from the heating element in DW.
Used to clean all kinds of electonics this way. Even $10K items. Make sure it is dry before you turn it back on.
I used to work for an aircraft company. We washed digital volt meters, counters, powersuplies and all kinds of high ticket items. Worked fine. It should dry in 24 hours unless it is completly sealed or you live in very high humidity area. Old paper or cardboard caps could be a problem. We sprayed them with a sealer. I dont think there are many around anymore.