As the Spider need not be elegant looking to perform well, dont bother about its looks.
In the model I originally built one and a half years ago (May 2015), I left the insulation on whip and radials.
Last month (Sept 2016), for experiment to demonstrate the affect of ground plane, I built another one. This time I removed the insulation from whip & radials.
I have noticed that men like the naked wire more than the fully covered ones, although the wires are not at all sexy .
Built One and A Half Years Ago (MAY 2015) - Using Insulated Core Wire
Built Last Month (SEPT 2016) - Using Core Wire With Insulation Removed