Yes on the former, no on the latter.
Then I think you would be hard pressed to define yourself as a "secular atheist".
If you believe in natural law, you accept at least some premise of moral absolutism that exists on a plane higher than humanity and the perceivable world. In fact, you apparently subscribe to a set of perfect-form ideals that likely will never be fully realized on this plane of existence, and I suspect that at least a few of our founders held the very same or similar beliefs, although would probably not have identified themselves as "secular atheists."
In any case, for me personally, it seems only rational that such immutable laws could only proceed from a "law giver," but others may come to other conclusions that they find more satisfactory.