Как отключить / запретить обычному пользователю доступ к настройке внешнего вида в 16.04 LTS

First of: why? They can't do any harm with it and you might think it is easy but you are forgetting a couple of things.

You do it like this ...

sudo chmod 700 /usr/bin/unity-control-center

This will prevent users to change any settings provided by the graphical interface but ... this will not prevent them from using command-line or a TTY. If they know how to use gsettings they can still alter any of these options. So you probably also want to prevent them from using gsettings. And a can of worms opens :)

Now for a better method:

Why not reset these settings you do not want them to alter on every boot? Just create a script with the gsettings in it.

gsettings set org.gnome.desktop.background picture-uri file:///dir/dir/dir/wallpaper.png

will change the wallpaper. Similar to that you can create lines for other options. Execute the script somewhere, and make the script non-mutable for normal users. This works if you only want a few settings.

If you really want to reset all settings: create a script to read all current settings and reload those settings when the system is booted.

--

Easier method:

cd ~/.config/dconf/ 
~/.config/dconf$ ls  
user
~/.config/dconf$ file user
user: GVariant Database file, version 0

... copy this file and restore it during a boot.