Dr Midnite is one of my favorites, but DD should have an advantage here.
He has better physical stats and martial arts training and the Doctor's black out bombs won't affect DD.
That said Dr. Cross has a chance using nerve points and his other equipment, grapling hooks, hidden bladed weapons and medical stuff to immobilize or put someone to sleep, but that all depends on how close DD goes.
I'd give Cross 1/10 or something, because DD's only equipment is his stick, but Cross has may stuff as standard equipment and can drug Matt if he lets his guard down. Plus he does know martial arts and nerve points (in JSA Classified he took out a vampire like creature and superstrong meta)