I found a question and answer that combined with the answer Pink
mentioned below, gives us the solution to your problem.
As Pink mentioned below, there are a number of good enzyme cleaners
that will get rid of cat urine by ?eating? it.
However, your problem is with wood and not carpet, so it?s going to be
tricky to get out because it has soaked into the wood. In cleaning the
urine from the wood, you have to get the wood damp enough the cleaner
can penetrate and remove the odor, but not so wet it warps or damages
?Wood soaks up liquids like a sponge, and cat urine can be a big
problem. Though it usually won't cause long-term damage to the wood,
the odor is unpleasant and hard to remove. In fact, chances are good
that you can't remove the odor entirely. If the wood ?does not feel
soft or have a problem with dry rot, you can try sanding the area and
then refinishing and resealing it with a finishing-oil such as tung
oil or polyurethane. Since you can't get the smell out, the idea is to
"seal it in."?
So, what I?m going to recommend is that you get one of the products I
list below, spend a couple days maybe wrapping a damp washcloth with
the solution to the wood for 15 minutes at a time and letting the
cleaner soak in, then turning a fan on the furniture to let it dry
between cleaner applications. Before doing this, I recommend a test
spot to make sure it does not discolor your wood.
Then gently sand the wood, and re-finish to seal in any remaining odor.
Here are some product suggestions you can try.
White Vinegar http://rhol.org/rental/catodor.htm
Google Search: ://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=get%20cat%20urine%20out%20of%20wood&btnG=Google+Search
If this answer requires further explanation, please request
clarification before rating it, and I'll be happy to look into this
Google Answers Researcher