Differential mode could definitely do something, any picked up noise probably differential mode, but you want to keep the filter cutoff away from the audio band, since the input signal isn't differential.
That being said, what about an RC or LC low pass filter on the audio inputs? Won't do anything to protect against like power supply noise, but would effectively eliminate high frequency noise picked up on the input cables. Shielded signal cables or shielding for the amp can be a viable option, too.
Still, your best bet is going to be to scope it and see where it's coming from. With the gain options for the chip, you can probably still see noise on the inputs/power rails if it's significant on the output, so time-correlating them should show you where exactly it's coming from. Much more narrower scope (ha) of a problem to troubleshoot when you can identify where the noise is actually coming from.