The handle finish doesn't matter for food prep toxicity. I wouldn't chew on a BLO finished handle, but I also wouldn't chew on the phenolic resin of my Henckels, either. The problem here is that wood stabilizes differently based on species, grain, moisture content, temperature, et al before you even decide which chemical to add. Home-built vacuum rigs don't get the same level of penetration of the stabilizing agent--there's more to it than hooking up a shop vac to a plastic bag. Practice your process on something cheap, porous, with a loose grain, then cut it in half to check what you are getting. Then move up to tighter, denser wood. If you have a unique piece of wood that you want to get the most of, send it out to a professional.
This is a great post. I stabilized wood and other materials with home rigs for sometime when I was turning wooden/bone/horn pens on my lathe along with a bunch of other things. You can get a pretty dang good stabilized product if you are willing to put some money into the process and practice on different materials. You won't get the penetration of the professional stabilizers that have tons (literally) of pressure applied, then vacuum cycle. But you can get enough penetration to keep the wood well protected. I did a bunch of kitchen knives made with blade blanks I bought and used the home made stabilized material.
Now, if I am gifting a knife, I buy the blank then simply handle it the way I have my hammers, chisels, etc, that have wood handles. I use white oak, hickory, or other dense nut woods. For tool use that is exposed to all manner of sweat, rain, dirt, solvents, etc., the hickory or ash handles last until I break them.
For the kitchen knives I have handled, I use the same woods but treat them in a pan of mineral oil that is around 180 degrees. I leave the wood in for several minutes, and don't put it in the pan until I have finished shaping the scales. Since I glue and pin the scales, wipe off the back side of the scales with lacquer thinner to get them clean (like you would any oily wood) before epoxy application. I only drill one index hole for the pins for shaping, and then drill the others after the oil treatment is finished so there isn't oil in the holes before gluing. Never had a handle fail, and as long as they knives stay out of the dishwasher they last very well.
Just as a thought, think of all the kitchen knives (millions?) that have been made with wooden handles that are untreated nut woods. The Old Hickory line comes to mind, along with Russel brand knives (not A.G.) and decades old knives like Sabatier that used wood handles. A little care on these knives goes a long, long way.
Robert