If there is more than one channel that air can flow through, sticking a fan in just one will cause more air to flow down the others. It's parallel resistance, can you find the ohms? Or you could set multiple fans at the same time to balance out the disturbance.
Could you do better with pitot tubes? If you have small dia plastic tubing with one end in a water bucket and the other end crossways in an airstream, you can tell the pressure drop by how high the water raises from the surface of the bucket. Too much drop though and you could empty the bucket.