Pull them out roots and all or they will come back. If you get them when they are small the come out pretty easy. You may have to dig the bigger ones. No the plant parts aren't toxic to the skin as far as I know.

I raise rhododendrons and when I noticed some rhododendron plants dying, I noticed a couple walnut plants back in the woods behind the rhododendron bed with the dying plants. Since these were very tall established trees, I took the tact to girdle them. They still put out leaves the next 3 or 4 years, but dyed eventually. The rhododendron bed is now coming back. I lost some plants, but the rest survived.

Now I go out each spring and pull out all new walnut plants. If you cut them off, it is best to apply roundup to the stump to keep them from sending up shoots. They will keep sending up new shoots from any roots left in the ground. They are planted by squirrels and grow rather quickly from the large black walnut nuts. They are easy to pull out when they first germinate, but the roots soon get very attached to the soil. Try removing all the roots if possible or spraying with roundup. The Juglone eventually degrades and the soil becomes useful. Some plants are not affected by Juglone:

Here is a link that might be useful: Juglone Tolerant Plants

OK thanks! We will work on removing the saplings with the roots attached. I can't use Roundup since it's a chemical herbicide and there are many plants like peonies right next to these Black Walnut saplings. But I think I can pull the walnut saplings out with the help of a shovel since they are still pretty small. I didn't know that about the squirrels! That makes sense. Black Walnuts grow all over the place around here. Thanks for the info...

If you have to cut them down, you paint the roundup on the top of the stump to kill the roots. You can put foil over the roundup on the stump to keep any good plants from touching it.

Keep a sharp eye out every year - I thought I had removed several only to have them pop up again. This spring I was digging in the garden and found a Walnut, probably buried by a squirrel, in the process of sprouting right under my nose. These trees are pests and there is almost no stopping them. When I use Roundup, I put a cylinder of any sort, such as a narrow cardboard box open at both ends over what I am spraying , spray the plant and leave the cylinder in place for a while. I bought a jug this year that has a foam option on the spayer, which is heavier and doesn't disperse as much.

Not only do you need to kill the tree and roots, burn the stems that you cut down. They will come back with a vengence from tree stalks and leaves. We learned this through experience.