White barrels are going to be tough to get. Whites aged in barrels are generally Chardonnay's. they get their fermentation and aging done in the barrel, maybe a vintage or two to tske the sharp wood bite out of the new barrels, then they get transferred to the red side of the room where they are still good to go for many years. Barrels used only for whites have a lot of life left in them, they'll be dear.
Look into Gibbs Brothers Barrels in Arkansas . American oak, charred how you want it. Prices are good, shippings not bad and it's brand new.