FreyrStrong, I wouldn't attempt any polish. I'm firmly of the opinion that you shouldn't use any polishes or solvents on a sword, and you should just oil it lightly to stop rust from advancing. But I can see you have already discovered the range of strong opinions on this topic.
The problem with camelia oil, although it's traditional, is that it is organic and therefore decomposes; You have to remove and reapply very frequently which is fine if you're using the sword and thus doing this anyway. Mineral oil is better and of what choji oil consist these days (with clove oil for scent).
I inspect, clean and oil all my swords once a month. It takes hours because after doing this, I vacuum heat seal them in heavy duty polythene bags with silica gel desiccant pouches! I'm considering filling the bags with inert argon instead of trying to remove air! Yes, I'm obsessive!
Get yourself this excellent book by a materials engineer, who dispels many of the ideas surrounding sword care and gives better alternatives. It's full of graphs and loads of lovely empirical data:
Analysis of the Iai Katana
For example use thick microfibre cloths to remove oil rather than uchiko powder (which is by definition, abrasive). Use modern rifle oils, often with powerful rust inhibitors, rather than vegetable oils etc. I use a mixture of mineral choji oil and a bit of rifle oil.
Renaissance Wax I am more ambivalent about, but my default position would be to avoid using anything on a sword other than camellia oil, the "clove oil" that sword shops sell, or light machine oil (like sewing machine or electric shaver oil).
If it's good enough for the British Museum/Victoria and Albert Museum and has His Majesty's Royal Warrant , it's good enough for me! It's also entirely removable as all museum restoration substances have to be.
Actually, some of the commercial "clove oils" that are sold from Japanese sword shops are just camellia oil with some drops of clove oil put in for scent. Anyway the sword only needs a very thin film of oil. It's not good to have so much oil that it pools up where gravity takes it.
I used camelia oil for a short while but was alarmed at the way it beaded on highly polished blades (cohesion) leaving some areas
apparently untreated. Then, I couldn't easily get it all off (I think I had to use alcohol in the end) before I went back to (mineral) choji oil.
But, just do what you think is best.