I don’t know why one would assume that the oil used on wooden cutting boards comes from pigs.
Oils most commonly recommended for wood items that come in contact with food – like cutting boards – are:
1 – White mineral oil, a petroleum derivative
2 – Pure beeswax – Rav Dovid Heber states that it’s kosher
3 – Coconut oil
4 – Carnauba, from palm tree
5 – Tung oil (no, not tongue), from Tung tree, bad for
those allergic to nuts
6 – Linseed oil (raw, not boiled), from flax plant
7 – walnut oil
8 – Shellac or lacquer, which is a secretion of the lac insect and Rav Dovid Heber quotes Rav Moshe as holding that it is no different than honey in this respect and is a kosher product.