How can I silence this noisy SMPS board?
The noise comes either from the ceramic caps (due to piezoelectricity) or magnetics (due to magnetostriction). If it's the caps, you could change them for flexible termination ones which are designed to prevent vibrations from propagating to the board. If it's the transformer, you're screwed.
The document linked in the question does not mention how much current this power supply can output, but a 5V 50W power supply of good quality costs about €20, which means replacing the whole board may be a reasonable option.