Walnut oil is particularly quick to go rancid, so it might be worth taking a few steps to reduce the amount of metal that gets into the oil. Maybe a press made of stainless would be better in that regard, than one made of carbon steel, but I really don't know.
This might not matter: if you're using it right away, on salads, there's no problem, and if you're storing it for use as a furniture finish, the worst case is that you'll get "boiled" walnut oil. But storing it for food use might be tricky.
"the qualities of these bacteria, like the heat of the sun, electricity, or the qualities of metals, are part of the storehouse of knowledge of all men. They are manifestations of the laws of nature, free to all men and reserved exclusively to none." SCOTUS, Funk Bros. Seed Co. v. Kale Inoculant Co.
Best is BHT, which by the way is non-toxic and incidentally, prevents cancer and herpes. But it's slightly bitter, so best to use a synergistic blend of 5% BHT, 70% A.P, 25% Taurine. 1/4 to 1/2 tsp per litre.