Hi Cam,
the #81 Hand Polish is a non-abrasive polish and contains no chemical cleaners either.
That said, just the act of rubbing some type of liquid over a waxed surface tends to have a cleaning and polishing effect which is either accentuated, or diminished depending upon your application material, and your application procedure.
Apply the #81 Hand Polish with a soft gentle motion, using light pressure on a soft clean foam applicator pad and it will probably not remove all of the coating of the #16.
Apply the #81 Hand Polish with a wool cutting pad on a rotary buffer with heavy pressure and it will probably remove all of the paint.
Application material and procedure are a factor to how aggressive any product is.
If your goal is to completely remove the #16 Professional Paste Wax, then I would opt for using the Deep Crystal Paint Cleaner with a little elbow grease, or even ScratchX.
Mike