I would use a fairly stiff length of electrical wire to poke it out, from the button side downward toward the tenon. It's advisable to test an inconspicuous spot on the stem before using any solvents, but it may help to moisten the blockage using a pipe cleaner soaked in lemon juice if the stem is vulcanite or ebonite, or alcohol if it's perspex or acrylic.
The same advise would apply if you were referring to the shank, though I might be tempted to use an appropriately sized twist drill -- employed manually, of course.