Disabling Voice Control, or at least muting it (iOS 10)
As of iOS 10.2.1 (maybe as early as 10.2), it is possible to disable Voice Control.  

Settings &gt; General &gt; Accessibility &gt; Home Button


There is a setting PRESS AND HOLD TO SPEAK.  Set this to Off.  The descriptive text is "There will be no response when you press and hold the Home button."

I would like to thank Bob Briscoe for providing this answer, which he received from Apple Support. Since the question is protected, he cannot post an answer himself, so I am posting on his behalf.