Giving birth is real great moment and today will definitely be a day to remember. I'm not married yet and so don't have a child but I had a first hand experience two years ago when one of my aunty wanted to deliver.

She was expecting the due date to be in like 5 days time so nobody expected the baby to come that day. The husband has left house for work very early in the morning. She started having the feeling around 8:00am but she taught it was nothing serious. I was called out from my room around 10:00am to come and drive her to the hospital. I was with her with one of my sisters. To cut the long story short, she delivered the baby right in front of the hospital before we could carried her in. We had to rush in to call the nurses outside to attend to her and take her in.
She is such a strong woman. I've always heard but not seen a woman giving birth on her own. That was my first experience. It's was just easy for her. I was told she gave birth to her first child easily too.

As you said, let the nature run it's course.

I wish your wife a save delivery