Your correct about there being two types of plastic, one good, one not so good, I would take it to a specialist paint/repair place as if you overheat the plastic, it can become brittle etc.
http://www.bikemedic.f2s.com/graphical/ http://www.ryebrookpaint.co.uk/fair.html Just google fairing reoairs, there are a lot of places.
Chris
