There can be a little click with these amp modules - but nothing which harms a tweeter or speaker. They don't have relais at the output which is a big benefit (cause they get bad over the years) - so I for sure take the little click instead.
The module itself should achieve 123dB S/N - the input of it is differential, maybe the unsymetrical input is catching some humm. Speakers with "normal" sensitivity will not make that audible in some distance, with high sensitivity speakers you could try the symmetrical version, it could be better there.