Any of the three oft-mentioned hospitals would support a completely natural birth as long as Mom & Baby are doing well.
And, any old nearby hospital will do if there is an emergency! The Duchess of Wessex nearly died having Louise but the doctors were able to save both of them in a very dicy situation. She was so pleased with their care, she returned to have James at Frimley Park. (sic?)
I'm sure Meghan will sail right through this birthing lark. Obviously, she has been healthy throughout and if there was any question of a normal delivery, the decision would have been made already. Doesn't mean they have to 'share' though. lol