Should you decide to use your Kitchen steel for sharpening your tools I suggest you wash the steel sharpener in hot soapy water when finished.
There is a possibility to transfer even the smallest amounts of Boiled Linseed oil Wd40 or whatever you use for metal protection onto your kitchen cutlery.
Might sound silly but I am experimenting with a combo of beeswax, flaxseed oil and a dab of vaseline to protect my axes and sheaths.
Reason being if I ingest any of above it is food grade and wont do any harm. Just the other day I was screwing around cutting up carrots,taters and meat with my ax just for fun and I also use my axe sometimes for food prep when camping. Alright I'll shut up now.