The CS could easily handle the thin lines if using a thinned paint being shot between 5 and 8 psi. The real problem is control. Are your hands steady enough to do fine line work like that?
I find eye veins are best done with a round, 5/0, camel hair brush. The near-needle point of that brush is perfect for a job like that. They're a little more expensive than regular, run of the mill paintbrushes, but they are so worth it.
Very rarely will a job ever be done with one kind of tool. I've been airbrushing for the better part of 2 yrs now and I don't think I've ever done a project that was strictly all airbrush.
But don't get me wrong, I'd love to be able to add a micron C and an eclipse CS to my collection one day. Between those three (micron C, eclipse BCS and CS), there shouldn't be any project you couldn't handle.
-Fred