After much searching, I've found only one method to disable the touch feedback sound. Unfortunately, it requires a Windows PC. Although this does not answer my question in the OP body above, I thought I would share it anyway, for lack of a better solution:
- Go to: https://www.microsoft.com/hardware/en-us/p/arc-touch-mouse#support
- Select your Windows OS variant in the drop-down box
- Download the Mouse and Keyboard Settings software
- Plug the Arc Touch Mouse USB dongle into your Windows PC, then wait for drivers to install automatically
- Install the software (ignore the reboot prompt, rebooting is not necessary)
Open the Mouse and Keyboard Settings, and look for the Vibration setting towards the bottom:
Disable the vibration setting by clicking the switch to the off setting.
Unplug mouse, and plug it into your Linux computer
Voila! No more artificial scroll-wheel sound!
I don't yet know of a way to do this under Linux only. I searched Github and Google for open-source alternatives to Microsoft's Mouse and Keyboard Settings, but have yet to find anything. You could try running the Mouse and Keyboard Settings application under WINE, but I have yet to test that.