I’m a Carbon steel kinda guy !!
I believe you can eat Mineral oil as it is sold in the pharmacy as a laxative. In addition it is supposed to be tasteless. Olive oil has been reported to work well as well but I would worry about it becoming rancid.
Tuf cloth is GREAT for carbon steel knives and although it has not gone through FDA approval its makers claim it is safe. I have even used it on carbon steel around sea water and worked great. It is what I currently use on my carbon steel straight razor that I use every day to shave.
Keep in mind that you need the thinnest of coating of either of these so it shouldn’t to adversely affect your leather sheath.