Pretty sure most of you already know this but for those who don't: you have two clipboards in Linux. One is the traditional clipboard where you copy with control c and paste with control v. The other one is when you highlight text and use the mouse middle click to paste text.
More details here.
Whenever I use a touchpad without physical buttons, I usually disable the middle button entirely. It's more of a hammer-to-mosquito solution than what you were asking, but it's as easy as adding this command to the autostart file (on Xorg):
xinput set-button-map "Name-of-your-Touchpad-goes-here" 1 0 3 4 5 6 7, where "Name-of-your-Touchpad-goes-here" can be found withxinput list --name-only.