Hmm... Don't know anything about acoustic pickups but, I'm guessing the same principles apply. With the pickup being a single coil it's going to have some static or hum. I'm guessing that's what you're referring to?
Wait, is this static, or hum? The Woody is a single coil pickup, so there will be hum. As far as static...like when you move the cable? I am having a hard time understanding what this might be.
I would first check the amp/mixing board or what you use for amplification/recording with another pickup or guitar. Then i would check the cables and connections for noise (wiggling and shaking).
No other guitar to try but thought we would try another pickup. Don't have it yet though. If that doesn't work, guess we just have to live w/it. A better p/u is beyond what we need for our purposes.