JSWolf:
Yes that corrected it for me. Even after installing Calibre 3.8 and unpinning then repinning the button to the taskbar (as it happens I did that from the Start menu with Calibre not running) I still got two buttons.
But if I unpin it then pin it from the running instance of the button on the taskbar while Calibre is running (started from the Start menu) the issue seems to have gone

.