40 lb breaking strain is probably not enough.
Given that you've got a 40-50 inch long sling with a 2-3 oz weight at the end.
You want to missle to end up 350 plus metres away. That's a lot of stress on the cord.
Now it might not add up to 40 lb, but if you get the slightest nick in the thin thread you're 40 lb drops to the point where it's most likely going to snap.
Braid it and you should be okay.
Plus for distance slinging as long as you are not using rope and a big old treb pouch - air resistance is not really an issue.
You might get a %5 distance increase by going from 2mm paracord and a slim leather pouch to carbon nanotubes and custom fitted netted pouch.
But with proper distance slinging it's almost 100% down to technique.
Make the most technical slings you can and you'll still have to spend years honing your slinging technique - there are no shortcuts in slinging
I'm not saying don't do it - just telling you it won't make you a better slinger.