Victorinox oil works well and is food safe.most light oils work too
I use 3in1 for my Leatherman MTs. I add very little to the pivots from time to time and when I get a new to me LM MT, I always clean first then add 3in1 oil to the pivots and give the whole tool a little wipe. I'm not overly concerned with food safe on those. On my SAKs and Trads I use a very light drop of Mineral oil. I like to use something that I'd be able to consume since the knives will be in contact possibly with food. I use my can opener on my SAKs but I don't use my blade on food necessarily. Regardless I like to use a food safe oil.
I just used 3-IN-ONE on a Wave I recently acquired which was stiff in places.First I soaked it in water with dish detergent, then scrubbed with an old toothbrush which was luckily all it needed to remove any dirt, then dried it the best I could with a paper towel.Next I sprayed CRC 5:56 (I don't have WD40) into all the pivots to help free them and also to displace any moisture still in there. I worked all the moving parts repeatedly then wiped off as much as I could.Lastly I worked 3-IN-ONE into all the pivots and wiped off the excess.It all moves much more freely now although I may loosen one of the pivots as some of the internal tools are still a bit reluctant to come out.I'm not saying you should do all this, it's just what I did. You could probably just go straight to the oil.
I use 85 weight Nano Oil on damn near anything (it's thick enough that it even does a passable job on torch threads), it seems pricey at first but I'm about a 3rd through a syringe thing that I bought 6 years ago and lets say my collecting problem hobby is in an advanced state