Hey Rick,
I stayed in Turtle Beach in October '15. There wasn't much encouragement to do shore diving, however the beach that you overlook is shallow and great for snorkeling. It would be quite a kick out for scuba depths (or you could dive for a couple of hours on a tank at pool depths). Your call. One of our group was a bit rusty and we did a check out dive off of White House Bay, just north of Salt Plat -- just beyond the Great Salt Pond (Between Turtle Beach and Baseterre). Again, shallow but plenty of life to see.
I lucked out and called Scuba Safaris
http://www.divenevis.com/ at Oualie Beach on Nevis. The problem with Turtle Beach is that it is a 30 to 40 minute drive to Basseterre to meet up with Kenneths or ProDive. Whereas Scuba Safaris picked us up at the Reggae Beach Dock -- 5 minutes from where we were staying (especially if you cut thru the dirt roads). They were a few bucks more expensive, but the convenience made it worth it to us. Nitrox is available. Douce (captain and dive leader) had a sling for lion fish on every dive. Valerie (Instructor/DM) made ceviche for a snack on occasion from the lion fish take. The shop rented us tanks that we returned the next day when we went out on their boat again. RE: spear fishing, St. Kitts and Nevis isn't quite as heavily regulated as some of the other island countries; so reasonableness rather than regulation is kind of the formula. So it is kind of more up to the dive operator instead of a patrol boat. You will be judged by your dive skills and personality. Remember, you are a LONG way away from help if you are hit with a lion fish spine.
The only other recommendation is when you rent a car, don't rent from Bullseye. Nice enough people, just not good vehicles.