Hmm... that's a good guess. I don't know the reason he did it. Confucianism was very popular at the time, so that may indeed have been an influence. What is strange about the action is that Buddhism and Shinto were basically the same religion at the time. So for a ruler like Mitsukuni to make a distinction and repress one of them is a little strange. I didn't mention in the article above, but Mitsukuni also helped compile a major history book about Japan. His book would later be used in the Meiji period to fuel nationalism. I wonder if compiling that book influenced his views — ie Buddhism, being non-Japanese, is bad, while Shinto, being Japanese, is good — which again would kind of be a preview of the ideas that took hold in 1868. The irony of that idea is Shinto itself is also a foreign idea, originally coming from Chinese Taoism, long long ago.

The implication of "swerves away / air in my hand" is that he was trying to catch the firefly with his bare hand, grabbing at it. The bug moved out of the way so he missed and ended up with nothing but air in his hand.