I like my Surface Arc Touch mouse. I bought it with my Surface Pro 2, but I don't use the Surface very much these days. However, the mouse does work perfectly fine with my Lenovo Yoga 900, and as a Bluetooth device it's way more convenient than carting around a wireless mouse that needs a dongle plugged in to the laptop to work.
But one thing that annoyed me about the mouse was the noise it makes when you use the touch-scroll strip. It's not a big deal when you're working in a noisy office, or at home by yourself, but today I'm working out of a public library and don't want to bother the people around me with the noise.
Now, I do remember looking into this some time ago when it first bothered me, and not finding a solution. Either I wasn't looking hard enough, or the solution has come along some time after my initial investigation. Either way, it's an easy one.
Simply go to the Windows Store and download the Arc Touch Bluetooth Mouse app.
After installing and launching the app, all you need to do is switch off the Vibration/Sound setting. I turned it off entirely, but if you still want to feel and hear it a little bit you can adjust the slide down to whatever level you're happy with.