Mineral oil is fine for a fingerboard, but there is a caveat. Being a non-drying oil, it won't dry and nothing will stick to it. So if you put mineral oil once, it is mineral oil forever. If you try to put linseed oil or tung oil on it later, it will not adhere.

I use boiled linseed oil and beeswax on the fingerboards of guitars I've built. Linseed oil is a drying oil which will polymerize when it reacts with air instead of going rancid like food oils.

Drying oils or mineral oil should both work for the job as long as you do not try to mix them.

Wait a moment. Mineral oils are food-safe?

Don't they accumulate in the body and act as endocrine disruptors?