My OPINION, heavy on the O, in a drafty house (like mine) an oak is not needed, especially if you have or plan to have an APU hooked up for a power outage situation. I do not run OAKs on my stoves as my house, though a week or two newer than yours, is very old and has no wall insulation. It's been added on to a few times and all that sorta stuff.
I was home when we had a power outage and my stove had enough draw in the chimney to pull all the smoke out. I have just a few feet (I think 6') of vertical pellet type double wall chimney. It was warm enough that when the power went off, and the fans stopped, the fire pot smoldered and the chimney pulled that smoke out instead of coming back thru the air inlet and into the house. So that is a risk of not running a OAK.
But there are several threads on this site listing issues with burn quality in windy situations. It makes sense when the oak is right on the outside wall and the pressure changes with each gust. Think of it like standing outside in a windy snow storm. If you turn your back to the wind, the snow will pull up at your face as there is a lower pressure area in front of you. If you turn into the wind, though you will feel directly the force of the wind, less snow will make contact with your face.So when the wind blows by your OAK, one time it will push air into it, next time it can pull air away from it. If you do prefer to run an OAK, and it is just the one stove that is giving you fits, see if you can put some sort of temporary wind box around it and see how it works. It does'nt take much. Anything you have sitting there like a couple stack of flower pots etc. just to break the velocity of the wind right next to the OAK inlet.
IMO.