Well, my design should draw very little power so long as the CMOS 555 versions are used. However, if you want to drive an 8ohm speaker, that will use excessive power. A piezo transducer is what you want, it should be able to be driven directly from the logic gate output, or for more volume, use a discrete MOSFET follower.
3v is a bit difficult, it might work, but the battery voltage will drop over its life, and the operation will probably stop fairly quickly. 5v+ is more suitable.