I'm sure someone will chime in who has more experience with 5160, but with my HI khukuris, I try to keep a coating of oil on them, and they seem fine so far, even with the heat and humidity here in OK. I wipe them down with three in one oil, or remoil, or whatever I have around after I use and clean them.
As these are cooking knives, I would suggest food grade mineral oil.
Oh yeah, and a mirror polish will tend to be a bit more corrosion resistant than satin/brushed/hand rubbed/etc. Mirror polish seems to leave less microvoids which trap the water and help corrosion.
That being said, if you clean them well, dry them well, then oil them after each use, the microvoids also hold oil better. SO it's kind of a tradeoff.

I think if you coat them with mineral oil after use you'd probalby be fine.
last comment, is that at least with my hunting knives(all high carbon), I like the patina they start to get. I tend to use them in kitchen too, at least when I'm preparing stuff for dehydrator, as my Buch and Schrade hunting knives just seem more useful at times than my kitchen knives(esp. when cutting up steaks for jerky). But with the fruit juices, and blood and stuff the schrade has a nie patin. polished it off once or twice, then realized that it showed exactly what it was, a high carbon knife that actually got used, rather than sitting on a shelf. After that, didn't really mind.