An even cheaper solution is to buy a cheap emergency light that is intended to light automaticly in case of power failure.
Remove or dissconect the lamp(s) and connect instead a noisemaker of your choice, taking care that this is of the correct voltage and draws no more current than the lamps.
If you wish to silence the alarm before the power is restored, then fit a push to break switch in one of the battery leads.
Pushing this will silence the alarm, it wont resume sounding when you release the switch because the internal circuitry will prevent this.
When power is restored, it will work again as before without having to reset or restore anything, unlike a latching switch which might be left turned off.