Scott, you might try some CLR if you happen to have some around. The same product chemically (phosphoric acid) is sold by a lot of different companies under a lot of different names. You do want to test a small section first particularly because different woods also have different chemical constituents. Various other chemicals can do strange things to wood, like ammonia permanently darkens oak, so test first. After any time that you put the acid on wood, rinse it thoroughly. Wood acts like a slow acting sponge. It absorbs humidity but does not absorb water quickly so it will be OK in most instances to wipe the wood down with a wet sponge, but then wipe it down and dry it off.
If I knew more about what you were doing exactly, I might offer a different direction. This particularly applies where you might be working with wood with any kind of finish on it. Water and finishes don't always get along and the finish and the acid may not either. Test first and be careful.