I don't think you can BYOB to any of the restaurants, but if you wanted some for your resort, you could probably get some at Publix on your way in.
If it's important to you to be alcohol-free, it might be worth a quick call to one of the restaurants you're planning to eat at that you would like NA wine & ask them if they have it or what their BYOB policy is in that circumstance. I have always found the folks at the restaurants to be very helpful. Don't bother with WDWD-DINE, they won't know a thing. Call the restaurant directly.
Good Luck.