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Camellia oil works great, you can get all over the net and I know SRD carries it. Any traditional blade / knife oil will work fine.

Use a good quality blade oil. Check Straight Razor Designs or Classic Shaving for some. Also tuf-glide works really well for me and it's not an oily product.

I've kept mine next to the sink for near two decades with no problem. A little oil sometimes and recently started using tuf-glide. My grandfather kept his in the bathroom next to the sink for 60...