Don't use Hammerspoon, but I've managed to create `sudo killall` keybindings with skhd by wrapping AppleScript.

    cmd + shift - 9 : /usr/bin/osascript -e 'do shell script "killall coreaudiod 2>&1" with administrator privileges'

Here's the relevant line from my skhd configuration. This does pop a password prompt, but it works. I imagine you could adapt this to fit Hammerspoon.

Just curious, why do you need to do this?