Wonder if you could put a dab of baby powder on the back of the button (while it's dry) and work it into the little crevices of the letters with a toothpick?
You could look in the cleaning forum. Might be some good info there. 

duggap said:Actually, I think your button is the model used directly after the civilwar. You can generally tell by the angle of the wings on the button. Notice yours are at about 9 and 3. These were made from 1875 to 1902. Still a nice find.