Mineral oil and Vaseline are the same chemical class. They are very clean, single chain hydrocarbons (they are not completely clean, so the occasional branched chain or aromatic is mixed in). Vaseline simply contains longer chains so it is more viscous. The next in this progression is Paraffin wax, which is obviously even more "viscous".
They are both equally harmless. The Vaseline will rub off less easily, obviously, but as long as they cover the surface, they will protect equally well. Same goes for the pivot, do you like grease better or oil? Take your pick.
They protect against rust by simply forming a mechanical barrier to water and oxygen. Things like Tuf-glide, Miltec etc. on the other hand usually have a chemical group that actually bonds (chemisorbs) to the metal surface while the other side (of the molecule) is some hydrocarbon or even better some flurocarbon which repels water and also forms a barrier against oxygen. They offer more complete and longer lasting protection, but usually they are also not as harmless either. They are usually called metallophilic (or MP) oils. The big advantage is that they will creep underneath water so that you can not trap water underneath the oil film. Other oils like engine oils (which I like to use on my pivots) have usually anti-oxidants as additives. They will scavange the oxygen trapped in the oil or on the surface. But if you are careful and don't let pits develop and dry the blade before you apply the oil, you should be fine with mineral oil. For lubrication specifically formulated oils have additives which increase lubricity. Again, some oils like Militec bond to the surface and reduce chance of mechanical break down of the oil film. Mineral oil should work just fine for your pivot, but you might find other oils to work even better. Mostly a matter of personal preference I would say.
If you want some pretty long lasting, harmless protection for your blade, you can heat some mineral oil and dissolve some paraffin wax in it and apply it while still warm. It will leave a very thin wax film. Way too much work for me though. I simply have an empty tin can that I have stuffed with an old T-shirt, so that a little bit sticks out, into which I have dribbled at least 100 ml of mineral oil. I simply wipe down my blades with that T-shirt/can after use. I use synthetic engine oil for my pivots. Synthetic oils usually have a slightly better lubricity and the additives usually found in engine oils to increase lubricity further and reduce oxidation might help a bit, too...at least that's what I am telling myself. I have never done a stringent comparison test.
Hope that helps.
Thanks!
