I'm not sure how many fasteners per side you really need, but my vintage visor had a bunch (13 per side, most likely *far* more than necessary) when I pulled it off a wrecked mid Dodge van.
I've seen as few as two fasteners per side, though I'd not trust that to be sufficient to prevent stress cracks. There's apt to be plenty of lift and flutter on something as big and unaerodynamic as a visor in such a turbulent airflow area as the front end of a van's roof!
In case you think the ends aren't going to withstand the stress of flutter without cracking out your fasteners, you may want to consider building some sort of block to support the very center of your visor to reduce flutter substantially. Here's the wood brace my vintage Dodge visor had in the center:
The form fit arc portion of the wood brace was in contact with the leading edge of the roof. It was held to the roof with two long screws. Ugly, but effective. The flat portion of the wood extended out over the windshield.
BTW, McMaster Carr sells the snap cap style screw covers which are used to create a more finished appearance on exterior screws:
http://www.mcmaster.com/#screw-caps/=yr4pgoTrucksnvans.com used to carry snap caps in multiple colors including chrome and gold, but they all appear to have been discontinued, at least from their website listings.