Hi John,
Working as a kitchen fitter I have fitted a few walnut work tops and have used the off cuts and the cut outs from the sink & hob for bread boards/chopping boards.
One option is to not finish it at all, it won't look as nice, but will be perfectly fine.
A second option is to use Food Safe Finish (Chestnut I think), which I have done many times.
I have also used tune oil, which takes a long time to dry, but seems to leave a more durable sheen that looks much nicer.
We've been using a couple of walnut chopping boards at home for a couple of years now. I oil them as required with Terra Nova Naturoil. My wife loves them.
My friend has some gorgeous sushi boards which are at least 80 years old and are oiled weekly with vegetable oil. Obviously you can see they have had a hard life, but they get washed most days and are still solid and straight
If you look at the "Boardsmith" web site you will see a lot of info about boards, timbers etc. Walnut is fine - frequently used for high end boards. You can buy board conditioning oils and waxes on-line cheaply that are food safe.
You could even use walnut oil, which dries (eventually).
When we used English walnut to make stool seats, some of us used walnut oil, others food grade linseed*. The linseed darkens the wood much more than walnut oil - so depends what you are looking for.
* Not that we intend to serve food on a stool, you understand, but food grade was to hand !