In theory, this circuit will not work because it needs a pre-amplifier. Supposedly, a 741 or any othe pre-amplifier is needed. As I said before, I don't follow the theory. I already verified that the pre-amplifier is not needed, just adjust the 10k variable resistor. In fact, You may not be able to get the circuit to work properly with a pre-amplifier.
If you connected the metal shell to circuit ground your noise would not only diappear,
That is because LM386 is a power amplifier. It is optimized for driving small, very low impedance speakers. It is NOT well suited as a microphone preamp. I believe we have said this before. But now you understand WHY we said it.