I'm in the same situation with my son. He completed his OW this summer. I had intended to give him a couple years of experience before moving on to the AOW. I also would have preferred him completing his AOW in Canada where he will be doing most of his diving. This winter we will be heading to Roatan and he really wants to dive with the sharks. That dive is 65'. We didn't want to take a chance the dive shop would enforce the PADI depth 'guideline' so I enrolled him in the AOW in Roatan.
Based on my experience on diving around the Caribbean, I would guess there is about a 10% chance that they will limit your son to a 60' depth. As I mentioned in an earlier post, last summer our family did a dive trip to several islands. My 13 yr old, OW certified niece was along and not a single dive shop cared about any depth limit for her. She did around half a dozen dives between 70 and 100 feet.
Worth noting that just about anywhere you dive in the Caribbean, you are diving with sharks... regardless of the depth.