Thank you - I had seen something about that Camellia oil when I was looking for the sickle but didn't know what it was.
For a time, my youngest son collected some replicas of medieval swords that are made of carbon steel. (He is an archaeology major at the University of Georgia, hence the interest).
To clean and protect them, he used mineral oil, of the type sometimes used to seal and waterproof wooden or bamboo cutting boards. It seems to have worked. I think that if I had a choice, I would probably go with the recommended Camellia oil if you can get it. Mineral oil would be a second choice. Get the cutting surfaces clean and dry before applying oil.
If at all possible, I would store them indoors somewhere dry and clean. A storage box with a gasket lid would help control the moisture.