unless ur drumsticks are made of metal or an alloy of some kind (Eg. Ahead Sticks) i dont see any reason why u should actually clean ur drumsticks, just storing it properly would suffice actually. and even if it were ahead sticks i don't think its practical cause after its worn, (which will be in a very long time) you would still have to replace the top part, and retain the shaft anyway.
abit off-topic, but since some1 mentioned Ahead drumsticks, i would like to ask why some people dont recommend them for usage?.. I ever heard tings like say breaking cymbals or smth?.. =X