I can't see an easy way to redesign it so the 555 isn't powered, when not in use. If the power is disconnected, when the switch is released, then it will stop producing the tone.
I wonder what impedance that speaker is? It's possible it's too low for the 555 timer to drive, at 9V, which is why it gets hot. This probably isn't an issue, given the low duty cycle.
The NE555 could be replaced with the low power ICM7555, but it won't be able to drive the speaker properly, so booster transistor(s) would be required.