Its been a long time since I played around with 'ray gun' circuits but a simple one can be made from a 555 and a few other components.
This one doesn't really need an on/off switch. R1 and C1 form a simple charging circuit. Once C1 is charged (apart from a small leakage) the current taken from the battery is minimal.
The switch needs to be spring loaded (trigger switch) so it returns after 'firing'.
R2 limits the current through the LED to a maximum of about 10mA. The 555 is connected as an astable oscillator with R3 and C2 determining the frequency. (these can be changed to suit). The output of the 555 is AC coupled to a 64R speaker through C3. (If there isn't enough volume you can try taking C3 out and directly connecting the speaker.)
When the trigger switch is closed the energy stored in C1 turns on the LED and energizes the 555 oscillator. The voltage across C1 will decrease quite rapidly causing the the frequency of the 555 to fall (a sort of voltage control monostable pulse) giving a 'pew' type sound.
To reload the trigger is released, the capacitor charges and you're ready to go again after a short charging time (R1C1)
For a 'machine gun type effect' operation.
C1 can be charged by a low frequency 555 astable (around a few hertz with say 80/20 space mark ratio). This 555 would be operated by a push to make switch connected between the 9V supply and pins 4 + 8 of the IC.
At first, trying to use some side effect, as the sounding inductor core, you will end with very low efficiency.
RedGrittyBrick already pointed you to some existing buzzers as small as you need. Here is another proof link, that demonstrates that such buzzers exists.
If you really want to try something in DIY manner and is dexterous enough to work with 5x5mm electromechanical devices by hand, you can try to design some small electromagnetic speaker from a small solenoid and some thin iron foil as a membrane. Optional an anchor with a small hammer at the end that to knock on the internal side of the enclosure.
Another option is to open the smallest accessible piezo-buzzer and to try to cut only one part of it.
But all this is a very fine work and not everyone can do it. And is it worths?
Best Answer
Building on soosai steven's answer, if you use a DPDT relay, you only need one capacitor:
simulate this circuit – Schematic created using CircuitLab
When the relay pulls in, the capacitor charges through the buzzer. When the relay drops out, the capacitor discharges through the buzzer again. The diode prevents the capacitor from partially discharging through the relay (and any other loads) before the relay drops out.