Baby oil is scented mineral oil, so you may already have some. A drop down the top, another up the bottom, one on the adjuster ring, and operate the moving parts. Give it a wipe down and it's good for months. Might never do it again unless something gets sticky, or the bottom knob squeaks on the final 1/4 turn lock down.
I also just ordered some sample blades, I got Gillette 7oclock yellow, Gillette Wilkinson sword, Gillette nacet and I have a pack of rapira super sweedish steel blades on the way as well, if anyone has any feedback on these blades, I'd love to hear it.
I've tried all those you named, with one possible exception. Gillette 7oclock yellow, Gillette Nacet, & Rapira super Swedish steel are good for my beard. Lots of variables, but many folks like these. Your beard type, lather, technique, etc has an effect on results. Gillette Wilkinson sword has two sources. The German blades are said to be acceptable. I have no opinion since I haven't tried them. The ones from India I am testing currently. Can't say I like them much. With an aggressive razor like a Fat Boy on number 9 I shave every other day. Yesterdays shave with an Indian GWS in a Merkur Futur clone (Ming Shi 2000S) on number 4-1/2 has stubbled up sooner than with other blades. To compare, that setting is like going to 11 on a Gillette adjustable razor.