Some occasional oiling of the bore is a good idea. We recommend using almond oil. Be careful not to jam anything in the small section of the bore at the top. The safest way is to get a thin dowel and tear a long 2cm strip of old sheet so it will fold over and back, then add a few drops of oil and work in. Sometimes we use a bicycle spoke with a smoothed off end and covered with masking tape to get into the mouthpiece end. Again a few drops and work in.
Outside of mute cornett: use a small wad of cloth and then the same as above.