We go to the Outer Banks every year, too, a bit further south than Ocracoke, just south of Cape Lookout on Bogue Island (Emerald Isle is the town where we stay). We rent a pet-friendly beachfront house and haven't had any problems with Riley.
We'll walk him for an hour or so in the early morning (very few people on the beach at dawn so we'll let him off leash to run). He snoozes during the day while we shop or do touristy things, then we'll walk/play on the beach again in the late afternoon and walk a final time before bedtime. That schedule seems to work pretty well for us - I don't even bring Riley's crate anymore, just make sure he has his bed.
Emerald Isle has a public beach, but very little public parking so most of the beachgoers are from the rental houses. Makes for a fairly empty beach at certain times of the day, which is pretty nice.
Pretty typical of late afternoon
ETA: Go to Ocearch (shark tracker) and look up Mary Lee. She's a Great White who has been cruising up and down the East coast. I think she actually went into the Ocracoke inlet a couple of months ago.