These branches are small enough to handle yourself? Remove before midwinter, using undercutting etc. to prevent tearing away of the bark.

Pruning big branches off of black walnuts is undesirable as cavities are liable to result. Pruning back sections of branches is also best avoided. Another of many kinds of trees that is best trained into the desired structure when small and then left alone.

bboy - Yes, the tree itself is only about 6"-7" in diameter and the branches I want to prune are all less than 2". I'm pretty sure that I can tell my neighbor that I'm waiting for the leaves to fall before I prune it.

Thanks for the information!

Our yard is surrounded by Black Walnut trees, touching the property line and directly under & over utility lines, & the neighbors never prune - they wait for the utility company to do it for free - resulting in alot of bizarre looking trees. (when the neighbors go on vacation I grab my ladder & saw...)
Anyways, cut off the whole branch all the way back to the next branch or limb, or it will re-sprout near the cut end & look goofy, & you'll be trimming that same part in 2 years.
(I think the utility companies only cut 1/2 the branch as a method of job security.)
Research on-line for a picture of what the branch "collar" is. Some trees got the cavities bboy mentioned when the branch was cut flush w/ the trunk or next limb, removing that protective collar.
And don't use the trimmings for mulch - the juglone could damage or kill some of your other plants.