There are reef sharks around at most islands, but usually so deep that only the divers see them. I have only seen 2 in 12 dives. One nurse shark (very common in the islands, but they are docile and prefer to hide and sleep under ledges in the reef) and one gray reef shark and he swam away so fast they only way I knew what it was is because he swam right past me. Unless you are bleeding and splashing about, 99.% of all sharks will leave you alone.
In Aruba, the dive shop I went out with said shark sightings are almost unheard of. Barbados, the water is a lottle cooler, so sharks are more common, but still unless you are looking for them, you won't see them. They are down deep and prefer to stay there. In San Juan and St Thomas I have heard of divers seeing them from time to time, but usually nurse sharks.
Nurse sharks are very docile and actually have no teeth, they have several rows of inward facing prongs made of cartilage. They suck their food in and mash it, not bite it. The worst they can do is break a few bones in the foot of the person who stepped on them.
If you see one, consider yourself lucky. Not in danger. The dive instructor who did my certification course said if you don't bug it, it won't bug you. He has been right so far.
You have nothing to worry about..