What is the quickest way to unmute the phone app on a locked iPhone?
I've struggled with the same for years--and just discovered an easier way.  Tap the home or power button to get to the lock screen, or on the iPhone 6s or 7 just pick the phone up so the screen "wakes up".  

You'll see the phone number you're dialed into and the current call time in mm:ss at the top of the screen.  TAP THE PHONE NUMBER and you'll get the mute/keypad/speaker/add call screen, all without unlocking the phone.