My husband and I just got back from our cruise including a stop in Ocho Rios and we did the Dunn's River Falls climb. We are not in the best physical shape but we are not elderly either (34 and 40 yrs old). I would say go for it, there are exits along the way up the falls for those feeling unable to continue. When we went there were people of all ages doing the climb. The guides are amazing and they are very quick to spot those needing help. They know the falls like the back of their hands and will tell you where to place your feet so that you don't have any surprises. The rocks are not slippery (the water is so clean it does not allow any moss to grow on the rocks).
I must admit we were sore the next day, the same way you would be if you went on a long hike for the first time in a long time but it was a good sore because it reminded us of what we had accomplished.
If you have any questions feel free to let me know...