Create an applescript like so:

tell application "System Events"

	key code 48 using {command down}

	key code 9 using {command down}

end tell

Save it as an applescript application, then attach it to the middle button using the Mouse preferences and "Other".

It's a hack: cmd-Tab to get to the previous application, then cmd-v to paste. :-D There's probably a more reliable way to do it but this is a start. It will break if you want to paste between two different windows in the same application.

You'll still have to do ctrl-C to copy whatever into the clipboard if you're in something that doesn't do highlight-copy (probably anything other than iTerm or X), but I just tested this by selecting in iTerm and pasting with a mouse click in TextEdit.