It turns out, a simple copy operation will suffice! With a little more snooping around on askUbuntu it turns out that all network connections are stored in /etc/NetworkManager/system-connections/, so I just need to copy them (root access required) around using any of the distribution methods I'd pick.

To document the settings (we love spreadsheets) a simple script (solved with a little help) one can use this script:

#!/bin/bash

#Document wifi passwords

echo ssid,password > knownwifi.csv

for f in /etc/NetworkManager/system-connections/*

   do

      ssid=$(awk -F= '$1=="ssid" {print $2}' "$f")

      pwd=$(   awk -F= '$1=="psk"    {print $2}' "$f")

      #We are only interested in password protected Wifi

      if [ x$pwd != 'x' ]

         then

           echo "$ssid,$pwd"

      fi

   done >> knownwifi.csv

echo done

You need to run that script as root and you might want to add additional values from connection setting. Opens nicely in a spreadsheet of your choice