There is already a 100uF capacitor between Vcc and Gnd, as it is recommended by the amplifier standard circuit.
As a "last resort" try a separate (linear) voltage regulator for the amplifier.
the amplifier generates some light noise incuding a tone around 400hz,
It is always better to tackle the noise problem at source, so a very small capacitor across each LED will slow down the rise time and thus reduce the high harmonics that a fast edge generates.
Are you kidding?
Putting capacitors across LEDs will maximise the switching surges that are going to be impressed on the power supply.
There is no resistor in series with the LED array.