You can run K&N filters dry. Not sure if its a good idea but there are plenty of dry filter options out there.
Having said that, if worried, a light oil coat is all you need. Will that do much and are you wasting money on the oil kit? or just keep it dry.
Perhaps the dry filter options use a tighter weave or other materials to achieve the same thing. Not sure.
Hers one example. Looks the same as a KN but again, maybe different materials:
https://afepower.com/afe-power-31-10...y-s-air-filter