Polar pattern can help but your best friend is proximity. Every time you halve the distance between the mic and source you gain 6dB while the background noise stays the same.
Look for super-cardioid and hyper-cardioid mics. The Beta57A is super-cardioid. The C1000S comes with an adapter making it super-cardioid. Positioning is important. You need to know where to aim it for the best rejection of the unwanted sound. The null of a super-cardioid is typically the surface of a cone about 128° off axis. Super- and hyper-cardioid mics have a small lobe of sensitivity 180° off axis which you have to consider when placing the source and mic. Narrow pattern mics can make it harder for a non-stationary source (like a clarinet or vocal) to stay in the pattern.
You might want to look into clip-on mics for the woodwinds.