Replacing the input capacitor is a sound idea

However, a word of caution: such simple filters will cause gradual phase change around the new crossover frequency which may make subwoofer integration difficult. For start, I would suggest an experiment: add the target capacitor (0.22uF from your example) in line with the input and then see how it works with your subwoofer. Experiment with the best sub crossover frequency and phase to see if you are happy with the results. Then, if happy, you can replace the Spark’s input caps.
You may find that your satellite speaker’s low end rolloff is a better match with the sub.
I am curious!