The magnet in a shake-light is large, and the coil probably has at least a hundred turns of wire. A magnet and coil that can fit into a battery is going to be much smaller-- and then you still have to fit in the rectifier and capacitor.
All of this in the AAA form factor? Implausible.
That could almost fit in a AAA. The capacitor or battery would be the largest part after the magnet/coil mechanism.