I would find a place near the airport to take him out for a quick potty break and put him back in the crate for transport. It is familiar and comforting to him. Bring a towel, or newspaper and if he has soiled his crate discard the dirty stuff.
I would call Delta and see where to go - I think it can vary. You can get through.
I would get there about an hour early. The USDA requires a puppy to be 8 weeks before he can fly though and have a health certificate? How did you work that out with a 7 week old?