Excursions through cruise line or not?

Hi everyone. This will be my first cruise with Celebrity and second cruise ever (recently did Utopia of the Seas). I am planning on booking excursions through Celebrity as I know the ship won’t leave without us. However, pricing can be more by booking through the cruise line.

What do you all do for excursions, do you book with the cruise line or externally? We are going to Cozumel, Grand Cayman, and Falmouth—I think I would be more comfortable booking through the cruise line for at least Cozumel and Falmouth but wanted to hear if you have ever done otherwise. Thank you!