The height of the fringing magnetic force lines are roughly equal to the gap distance, or 0.42mm. The thickness of the bobbin wall is 0.95mm, which is > twice the gap distance.
As such, the fringing field lines won't reach the winding.
As for the windings themselves, you really only need triple insulated wire on either the primary, or the secondary. Not both. As it is more expensive that regular magnet wire, I would only use it on your N2 winding. (And N4 if it's also a secondary, if you were using N4)