I'm not familiar with the "Quadoptic" specifically, but the general answer to the relay question is, maybe.
The relay contacts are designed to handle more current than the the smaller, weaker contacts generally found in switches. Switches are designed with ergonomics and style in mind, while relays are designed to do a job.
If the current draw of the new headlights is the same as the originals, then you probably don't need the relay. If the lights draw more current, then you will want the relay in there even though it will still be possible to run the lights on the switch alone. The switch will be able to pass a higher current than what it is rated for, but this reduces the life-span of the contacts; Plus, it's generally easier to change a relay than a switch in the future!
I'd probably use the relay whether it's needed or not.
On their death bed, nobody ever said, "Gee I wish I'd spent more time at work!"
'68 Sprite 1275
'76 Midget 1500