One noise gets to the amplifier input, it is no longer noise...the amp just sees it as an input that needs to be amplified. So, there is no way to get rid of amplified noise from the output side. You either beat it before the amp, or you live with it.

Twisted speaker wire, imo, is for cosmetics only. The voltage is higher and the impedance is lower, so noise being injected into the speaker wires is almost never a problem.

Toby