Is it possible to map the in-call mute function to button?

[wouldya]

no. directly on the screen when the active call window is displayed....
which is a white box displaying call information such as the name of the person you are talking to, phone number, call timer. At the bottom of that window there are two icons that represent speakerphone and mute.
The speakerphone option looks like a phone receiver with diagonal lines coming out of it, representing sound waves, and the mute option looks like an old time radio microphone with an X next to it. To activate these options... tap one of them on the screen. These are not the hardware keys flanking the directional pad, they are on the screen itself, which is a touchscreen (if you didn't know that).

Place a call and physically look at the screen for these two options.

As I said in the previous post, the center hardware button in the middle of the directional pad will also activate one of these buttons that is selected, which is shown as a blue border (Windows Default color) around the selected option. The default selection is mute. so when you are in a call, just press the center button and that will mute the call.

let me know if that helps any.