I can only suggest to avoid the shopping, avoid making eye contact. do not shake hands and do not allow yourself to be pushed backwards (non physical contact) by a pushy shop keeper. While jamaica is just beautiful, other islands may give you a VERY false sense of security which does NOT exist here. No horror stories, just a few close calls, much research of others close calls that carefully warn you to thoroughly screen before hand, any independent tour operator... as well as just avoiding the pushy locals. If you just do your vacation thing, money tucked away, no jewlery and have a litteral hand on the kids, you'll find walking to and fro any excursion safe, but hassled.
we couldn't find a suitable tour here (ages 11-78), so we just walked around.... did the approved shopping which was the worst safety wise of 4 cruises, went out on our own a bit... worse than beleize.... and headed to 'ritaville. Many posts are here about excellent tours but the pre and post approaches from the locals on these tours validate our interactions while just taking a stroll on our own.
From my recollection the canapy and horse ridding tours, booked through the ship are just fine. We're going on cruise #5, jamaica is the ONLY port I would never do with an independent operator. I know of many posts here that you can find people that did independent tours very happily. This is just ME. I remember a couple at our dinner table that had done the canopy tour via the ship and loved it!
So I'm just guessing you've never been here before, as many people will tell you after my post, they enjoyed it just fine, I'm only suggesting to be more careful here than other ports and give it thorough research to make a good, safe choice.
oh, and belated sinicere welcome. search the threads, you'll find a ton of info to help you plan!