Brian, just now seeing this, and I am afraid I am too late. But not to worry: even if I had been here in time I wouldn’t have been able to help! There really aren’t any wine shops worth a damn in the Outer Banks. I don’t know where you are staying, but at Nags Head, just after the bridge, where Route 12 north splits off, there was a decent little market that had a few will-do-in-an-emergency bottles, and in Duck, there is Tommy’s Market, which is the same.
I also can’t think of where one buys wine down there, and while this is not what you asked, if you’re a beer geek this shop has lots of cool stuff.
We go to OBX every year for a week or two, and to echo what Neal and Dave said, I have yet to find any wine shops down there that are worth a damn. It’s driving distance for us, and I’ve just accepted the fact that if we want to drink the good stuff, we have to pack it in the car. Told my wife if she wanted to drink well this year, she was going to have to use her small suitcase!
Not too late! We’re leaving next week & due to COVID-related flight cancellations, we’re now flying into Norfolk a day early & spending a day in Virginia Beach.
I’ll poke around, but we’re going to take everything except afternoon rosé, which I feel like I’ll be able to find somewhere. If not, it will be champagne o’clock every afternoon. 
What is wrong with White Claw?
This is kind of funny. I’ve never been to the Outer Banks but we joined four generations of my sister-in-law’s family at a North Carolina beach for part of last week (Sunset Beach, just north of Myrtle Beach). I had the chance to try White Claw for the first time. Perhaps not surprisingly, we went through the 18 bottles of wine I brought and there was lots of White Claw left.
Pack carefully. Many established OBX businesses refuse to serve men who wear sleeved shirts or non-denim shorts.
This is late, but in case others plan trips in the future, Trio Restaurant & Market is a legitimate wine (and beer) shop. It has a good selection of both foreign and domestic from everyday drinkers to high end offerings. The cafe has solid food and 24 taps for an excellent beer menu. Milepost 4.5, Kitty Hawk.