The long, stiff fluffy cleaners for saxophones are called padsavers. They do clean and dry the inside but should never be left inside the instrument. They are also difficult to clean. Small, stiff brushes should not be used, especially if the bristles are held on with twisted wire; they are for brass instrument metal mouthpieces.
…BG http://www.bgfranckbichon.com/. They also have a large selection of neckstraps and ligatures.
Check out Joe’s post on saxophone care.