I was told that if the excursion is late, the ship will only wait for me if it is an "official" one. what is the chance of it is being late.
The chances are remote, but it does happen on occasion, to both the ship's tours and independent tours. It's true that the ship will wait for one of their own tours.
I've always booked the ship's tours, just for that little added insurance. I'm very risk averse, and I'd rather not worry about being late while I'm on the tour. The ship's tours may well be more expensive than something you can buy off the ship, so you have to weigh your tolerance for risk against how much more you'll pay on the ship.