Hm... Thinking back to the days I spent in my dad's wood-shop....
It depends on what the wood was finished with. Some needles I've seen have an actual finish, like some kind of absorbed varnish, and some are just polished. That would make a HUGE difference in what you clean with.
If they have some sort of varnish on them, then a mild, low residue soap/detergent sprayed/applied to a wash cloth and not to the needles might be good for wiping them down with. This way, you won't have too much soap/detergent absorb into any spots that might be rubbed clean of varnish.
If they are bare wood that have been polished, then a good, high quality wood cleaner, designed for unfinished wood, should be fine. You just want to be careful about anything that might leave a residue on your needles. Many cleaners for unfinished wood have a "sealant" component to protect the wood that gets left behind in the cleaning, and that might rub off on your yarn, or discolor your yarn.
I would check and see if there are any good hardware stores in your town (smaller, mom and pop style, not giant ones where you'd be more likely to get service from someone who actually knows what they're doing and not highschool kids on their afternoon jobs... no offence meant, but experience here counts) or furniture/antique stores and bring your needles on a little excursion. Show them and ask what they'd think was best. Antiques dealers might be a good place to start, because they often have to work with restoring and cleaning wooden furniture/items without damaging them or affecting their value.
I have a grand time going to small, independantly owned hardware shops and asking questions, because the people there often arn't necessarily working for the high pay and are often VERY knowledgable.