You would use regular linseed oil; NOT boiled linseed oil. Boiled linseed oil has metallic dryers in it that make it dry quickly; in a few days instead of a month. These are nasty metals which you don't want to ingest. Regular linseed oil will take a long time to dry, but you can eat the stuff if you want, so it's food safe.
Regular linseed oil is what woodworkers use to finish wooden food related items like wooden salad bowls, salad forks and spoons that they make.
Actually, ANY drying oil in it's natural state should be food safe. So, you should also be able to use Tung oil if you can find it without metallic dryers already in it. Also, try any art supply stores for walnut oil or poppy seed oil, which is what artists who like to work in oils use. I think safflower oil is also an art medium. I don't know why artists prefer walnut and poppy seed oil to linseed oil, but if these more expensive oils dry faster or yellow less, they may be worth the effort of obtaining for this job.
So far as I know, mineral oil is used on wooden cutting boards and "butcher blocks", but my understanding is that studies have shown that unfinished porous wood cutting boards don't have any more living bacteria on them than plastic high density polyethylene cutting boards. My understanding of the reason for that is that wood absorbs moisture which bacteria need to thrive and multiply. Basically, wood's absorbtion of water makes a wood cutting board the equivalent of the Sahara desert for a bacterium. So, even though wood cutting boards get all cut up and you can't clean them as effectively as a plastic cutting board, they're just as safe to use. But, that's only what I've been told on DIY Q&A forums like this one, and I'm no expert on the subject.