M.M.
I lived in NC for 4 years and sadly your quest for sharks will only go answered at the aquarium.
Really only when there is a hurricane offshore do they come in close. I would not worry. But there are shark's teeth on shore so bring baggies to collect them.
Go to the Pine Knolls Shores Aquarium if you can. It is small but they have a couple pet tanks, rays and hermit crabs/starfish. They also have the cutest river otters. We were members and went just to have lunch sometimes.
THere are a couple mini golf places.
Our favorite was Professor Hacker's Lost Treasure, they also have GoKarts and Bumper Boats.
There is also Golfin' Dolphin.
If you want a side trip go over the bridge to Swansboro and Cape Carteret, to the south. THey have some great antique stores and little shops. I loved old town Swansboro.
On the North of the island is Ft Macon. That's cool to run around in if you need a distraction.
I don't know anyone who has surfed the NC coast. Snorkled and dived, yes, my hubby is a diver. THe waves aren't that big unless there is a hurricane.
Have a great time.
Added: THere is a great high end grocery store in Cape Carteret(?) just over the southern bridge called Lowe's Foods. Cross the bridge, go to the light and turn right. It'll be on your left.
Walmart is in Havelock on 70, Jacksonville on 17, or on 24 towards Morehead. They're all pretty far away.
Good thinking R. K, the Jacksonville Daily News should have beach info.