I have to finish an Arican mahogony farmhouse sink. Obviously it has to be non toxic and water proof. I saw African mahogony finished with teak oil and liked it quite a bit. Perhaps a Schlack over the top of it would work?
From contributor G:
Why does it have to be non toxic? Are they going to be eating off of it? Most finishes are non toxic when the solvents have gassed off. If this is going to be near the sink I would suggest a conversion varnish or a 2K poly. Even standard brush on polyurethane would work well. Schlack or as we like to call it, Shellac will not handle water at all. It is a very poor finish to use in a sink area.
Two thoughts - first go look at West Systems for thin fiberglass embedded in epoxy finish. They use it on strip canoes. The wood shows through but is fully encapsulated. The other thought is to leave the wood naked, but switch to teak, or something that handles wet and dry cycles with some grace. Epoxy the joints. Either way it sounds like something my old friend Phil (the Mad Designer) would have loved. He used to paint everything white and put in white carpets - it guarantees that they will be calling you back in a year.
No other finish provides the mechanical strength to prevent water penetration, and if water gets below a finish it will fail. Oiling either hardens producing a film that would lift or a non-hardening oil would be removed by the detergent used in the sink. Please specify what you don't like about the answers you have received.
To expand the epoxy solution, if you want the last possibility, you could vacuum impregnate the sink with a resin either as a complete unit or building it up of laminate and in effect turn the wood to a big plastic chunk, but finding the vacuum chamber, the right resin, buying sufficient volume of resin and keeping the sink from floating would take some doing and thinking. No matter what the sink will in all probability have a very short life. I think Woodpecker said it well.