For a start - don't waste any white wine on it. It doesnt really work for carpets, I can't imagine it working on oak. Plus, why not drink it instead?
I have absolutely no experience in furniture restoration/repair, so am only thinking out loud here.
I know that domestic bleach will remove red wine stains (amongst other dyes), so why not try a little on some scrap oak (perhaps with a splash or two of wine on it to simulate your clients' problem first)?
I imagine the technique will depend on whether the furnitures' finish or the timber itself has been stained.
Good luck,
Adam