Any dive-op (worldwide) that serves the general off-the-boat cruise ship diver is going to give you a fairly gentle dive experience.
If you have dealt with cold, fresh water lakes as you have, this should be a snap. You are going to have to muddle through your initial steps of adjusting your weighting for salt water and the very likely over-dressing... use of "too much wetsuit" will be likely.
Dive ops that handle cruise ship divers are well used to this. There is time set aside at the beginning of dive #1 for you to adjust your weights, some do this at the boat dock before departure. With AOW under your belt, this should be a two minute process, don't overthink it and always take the DMs advice. They have seen this 10,000 times.
In Cayman, at this state in your dive progression, it would be better to do the boat dive, you might actually see something of interest- very little going on that close to shore for most of the more well-known shoredive entries. With their gentle local waters, it would indeed be a good place to learn basic shore-dive techniques, but your AOW likely already taught you more than you'll need to know to "wade into the Cayman pool" from the shore. Go experience some well fitted-out Caribbean dive boats, see how they work. Cayman dive ops (in the Fosters type of volume model) are notoriously conservative, even for those divers spending an entire week, some would judge them as intrusively protective. In that light, understand that there is no need for you to express any concern of limitations to them, everyone showing up gets treated the same, Basic Cert to Course Director. They have their national rules, and that will be that.
In Cozumel, they are no stranger to Cruise Ship Divers. Explain your concerns (once) to the lead-man at the dive op, then when you are assigned a DM, re-check that with him as well. (It is useless to have such discussions with the on-ship booking agent, this person likely has never had their head underwater) Then pay attention to what the DM is telling you in the dive briefing. Don't fiddle with your gear, pay attention. Cozumel has the opposite reputation from Cayman in terms of dive-op policies, especially in terms of week-long visitors. They will still hover-mother day divers from Cruise Ships, but as for weeklong divers, you can do some pretty silly things without the DMs getting involved or saying anything. That is the subtle but very real difference, but absolutely nothing that should affect you.
I (unlike your son) am now a crappy swimmer as I'm physically an orthopedic train-wreck. Currents are a delight. Strength and physical ability is not applicable to currents, likely your AOW will teach that. Paying attention to the DM will be again very important, although they will not take you to much of a current (if any).
Have fun, use what you have learned. Caution, not fear.
Leave the u/w camera at home... for now.
