You could use a command, in addition to the "Recognition Global Hotkey" option (triggered using the same shortcut).
That command could then contain either a "Set Audio Level" action to mute the relevant playback device, a two-second pause action, then another "Set Audio Level" action to unmute again, or, if your music application responds to a given keyboard shortcut to suspend playback, a keypress action that presses and releases the keys for that, the pause, then another keypress action to resume playback.
The former mutes everything (playing through the given device, at least), but will always mute everything, while the latter would only pause the music, but if it was already paused would instead start playback unintentionally.