Golly, you are right. I never thought about the hemaphrodite aspect. I have a friend who had a dog like this (RIP the dog, not the friend). She had the dog desexed but I don't know whether it was a neuter or a spay.
My friend called the dog 'he' all of his life. I would suggest that desexing the new puppy prior to the age of 6 months would be a good idea. I'm sure you will love this new puppy regardless of his ambiguous sex.