If it's that old & plenty still solid, it will make a good working handle. You're right about the thickness, mill it down a bit on the fat side (6-8mm?) & go ahead with the work. I guess a lot depends on your intended use, cleaning method & climate variations over time & general use. It would be better to use a finish which is completely impervious to water.
An oil finish would be OK, but will need more care in general, & don't leave the knife in the sink over night! An epoxy finish (some type of complete encapsulation of the wood, end grain & fibers) would be a bit better, especially if you can vacuum bag the wood & have the resin impregnate the wood before it sets up on you. Also, water-thin CA glues (CYANOACRYLATE) can soak into the wood if used as a filler & provide a durable finish.
Sorry if it isn't a "complete" answer to your question, but hopefully you have a bit more information to work with now. Use what you have is still a good rule of thumb. If you can buy something a little better, go ahead & try it on some scrap first! If you're into science, do all of them, set up a test & see what works best (usually the most time & money at that point, unfortunately).....