Alpha particles are very heavy and cannot travel very far. They can be shielded by a layer as thin as a layer of dead skin cells. Ionization smoke detectors have a small americium source encased in a layer of foil and ceramic, which stops the alpha particles from traveling outside of the smoke detector. Because of this shielding, the smoke detector poses no radiation health risk when they are properly handled.
There is no health threat from ionization smoke detectors as long as the detector is not damaged and used as directed. Do not tamper with your smoke detectors, as it could damage the shielding around the radioactive source inside of them. There are no special disposal instructions for ionization smoke detectors. They may be thrown away with household garbage, or your community may have a separate recycling program.