I like to keep my wicked edge oiled, it does allow grit to stick a little bit, but it performs much better well lubricated. These are just my experiences, feel free to post your own suggestions.
For the two clamp screws I find wiping a light coat of a high grade oil keeps them turning smoothly and freely. I use a light coating of WeaponShield CLP, as it has EP additives, but any modern gun oil, grease would work well. The trick is you want something fully synthetic as I find it is easier to wipe grit off
For the pivots, I also used a drop of weaponshield, but I what I recommend just for the sake of keeping it clean is hornady one shot, it is a dry lube and keeps things smooth as butter but does allow shavings to stick. Eeezox would also work well however it can take a while to dry especially if you can’t wipe it. I wiped the arms with ballistol as it was non offensive, and easy to clean up, but this is another case where hornady one shot works well. After extended sharpening sessions I just wipe the arms off with a soaked cloth.