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?

Mineral oil is commonly used to coat/maintain butcher block cutting boards, and as a storage coating on high carbon knives. It is recognized as safe by the FDA when produced according to food safety guidelines and under quality control.

https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/cfr...

Food-grade mineral oil is highly refined and doesn't contain any of the carcinogenic aromatics. It could be considered a lower molecular weight petroleum jelly. It's also used as a laxative.

To my knowledge it can absorb a little through the skin but not through the intestines though more than a little will give you the shits real bad.