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I've also used Watco Danish oil, and 100% Tung oil. My intuition is that gdenby's observation is correct, that Danish oil may be more penetrating than pure Tung oil. I don't know which is more protective of the wood. I also agree that it is very important to seal the cracks prior to finishing the stick, if you plan to do that. I recently bought some Watco teak oil, but I haven't yet tried it.

Good luck with your project. Sounds like you will create a family heirloom.