I have the official K&N cleaning and oiling kit, and the oil does not seem to be anything special, and in fact, it's not even red. And it's not sticky.
I recall the red oil was a bit sticky, but the last time I used it was in the late 1970s so take that with a grain of salt.
The oil on the new filters was red and sticky - I've been too lazy to clean them so have been buying new ones, but I figured after 3 it's time to start cleaning them. The process to clean was no problem, I used a pail in the bathtub with the special cleaning liquid, which is probably just dish soap. Lots of rinsing from clean side to dirty side, and then a couple days of air drying.
The main thing I found in the filter was not dust or dirt, but insects.
Unless you are taxiing around in a very dusty environment, I think just about any thin oil is going to be fine in this filter. You'd probably be fine with no oil.