The issue with Leatherman tools and corrosion appears much to do with the brushed finish most of their tools come with. I reside in what could be considered a hot and perpetually humid climate, with a lot of exposure to salt spray. My full-size Victorinox multi-tools with their more polished handles and smoothly finished individual tools have proven to be nearly impervious to corrosion as compared to my Leatherman Wave and Surge.
You did not state how you carry your knife and multi-tool. If you are carrying them close to your body or even in a pants pocket, understand that human sweat is comparable to seawater in inducing corrosion, and that most common protective coatings you might apply, be they oils, greases or waxes may be quickly rubbed off or worn away in a pocket. Clear spray lacquer, paint, or some other air-drying finish would last longer, but I don't sense you want to go that route.
If you happen to be relying on leather sheaths, then you might consider replacing them with sheaths or pouches made of less hygroscopic materials such as Kydex or some other comparable hard plastic. An advantage to these synthetic materials is they can be readily rinsed off in tap water and quickly dried should they become exposed to salt spray or seawater.
But really, the simplest and single best thing you can do is to remove your knife and multi-tool from your pocket or sheaths at the end of each day. Even if you don't bother to wipe them down with a rag infused with a superior gun oil like G96 Synthetic, just having them air-dry will do much to avert rust and corrosion.
