Why does the client want to test the alarm in silent mode? It only takes a few seconds and has the huge benefit of familiarising all occupants with the sound of the fire alarm, its volume relative to ambient noise levels. It should not cause any significant disruption except in call centres and control rooms. In most workplaces I think it brings significant benefits.
Disable other outputs certainly- fire shutters, etc because these may well disrupt operations and will in any case be subject to their own, relevant test regime.
But if the weekly fire alarm test is to be operated in silent mode then I would take a look at what other arrangements are in place to ensure that building users are familiar with the sound and the thing remains audible throughout.