"Natural design" sounds like an oxymoron to me. A design is a blueprint or plan, as when an architect says,"Here's my design for the new building."
Natural selection doesn't design anything in that sense. However, if you look at something in hindsight, you can say,"The hawk is a great design, with its flying ability and super sense of sight. Nature designed the hawk very well." The IDer looks at "design" in this sense, in hindsight. They talk about the exquisiteness of this or that evolutionary development and say, "There's no way this could happen by chance. The odds against it are phenomenal. Think of the extraordinary complicated events that had to take place for the hawk to evolve." But of course any evolutionary development is "exquisite," when looked at in hindsight. In fact, any event is exquisite. If my mother had left 5 minutes earlier at that train station, and never met my Dad, I would never have been born. What an extraordinary set of coincidences had to occur in order for them to meet just at that point in space time! Obviously, I was designed.
"natural design" sounds like a sort of Life Force idea, as though nature said to itself, "I need something with hands, something that can pick things up. Let's work on that."