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Why not ask Black Wing if it is okay to use K&N oil? That is what I would do.
I'd give 99 to 1 odds they'd say no, even though the answer is yes. Because they sell Blackwing products, NOT K&N products. Id also bet the reverse would be true if you call K&N. This isn't a difficult situation, or decision. Filter oil is filter oil. It's not lubricating bearings. The gauze or cotton will never know the difference.....
I used K&N filter oil on my Blackwing for 15+ years when I ran that unit. And nothing was damaged or degraded as a result. Either K&N or Blackwing filter oil works just fine on either or filters.