What I don't burn in my fire pit when the kids want to roast marshmellows, I take by bags of sawdust to the local lawn waste dump...
I keep my walnut shavings segregated, and have a waiting list for it.
I understand that horse urine reacts with it to produce a toxin that is absorbed through the hooves of horses. Okay, no horse stables for me. even one that doesn't mind low levels of toxin.
However, walnut contains a chemical that prevents seeds from germinating. If you have a rose garden, you don't plant seeds, and all the weeds come from seeds, plus walnut shavings make a pretty brown mulch. Same for lots of other gardens grown from plants rather than seeds. I put an inch or so under my foundation plantings, and get very few weeds for the next few years.
I give it to my nasty neighbors for their flowers
Ron In Clanton, Alabama
Shoot amongst us boy, one of us has got to have some relief!
I toss it out in the "green" barrel. I also shake the bags out real good if I plan to use the next non-toxic batch of sawdust in the garden.
"A hen is only an egg's way of making another egg".
– Samuel Butler
Depending on the sizes of your "end use" Walnut, and whether you get it green or not, I save mine and then pack my "green" pieces in it to slow dry. I do the same with Maple and other woods though Walnut is the only one I will segregate from the rest of the shavings/chips. I use cardboard barrels which let air in and out extremely slowly and the pieces get a chance to dry evenly. Works for me, YMMV.