Oregon Inlet (the Fishing Center) is great for wade fishing, but not so much for paddle boarding. I’d look at Salvo Day Use area which is further south from Oregon Inlet, but only by 30 mins. If the wind cooperates it’s well setup for paddle boarding and there’s a lot for you to access wading. My dad and I have caught a lot of fish from there kayaking. There’s a public spot at the end of W Danube St in Nags Head that looks like it would be good for both, but maybe have a look for yourself before committing. It looked decent when I scoped it out for kayak fishing, but I’ve never tried it.
You can’t go wrong with an 1/8 to 1/4 oz jighead with a 4” Z-Man or similar soft plastic lure. I like paddle tail, but there are others. Let it hit bottom and bounce it back. A popping cork is good, too. Same jig setup as above, but suspended 18” or so beneath a cork. The tackle shops sell the cork you need.