So, what we are going to do, is just assigning an unused key, for example the <Menu> key, or a key combination to a keyboard shortcut for the command:
xdotool click 2
You need to install the package "xdotool" for that:
sudo apt-get install xdotool
Unfortunately, assigning a modkey + mouse-click combination is a bit tricky and doesn't work reliable, depending on how fast you release the respective modkey, and there is also the potential to screw up the state of those modkey. Also, because of the default modkey + mouse-click combinations, only the right-click comes into question for such a combination. Just in case you want to try that, this is an example for a needed extended command, in this case the modkey is <Control>:
xdotool keyup Control; xdotool click 2
I recommend setting up any of those shortcuts in "CompizConfig Settings Manager > Commands", but you could also set up at least the keyboard shortcut in "Keyboard Shortcuts".