I honestly listen to nothing. I don’t even let the water run unless I am cleaning soap off my razor. I can judge how close my shave is by the sound of razor on skin. Maybe I’m a shaving whisperer.
I also listen to the audio feedback of the blade cutting, because it helps. Sometimes you think a bit is perfectly clean, but "scruunch..."
As for razor rinsing, I use a 1L polythene container of hot water, so that after the shave I can empty most of the tiny but unpleasant shards of keratin into the WC, and reserve my clean sink of hot water for face rinsing,
I love my audio collection outside the bathroom.