How exciting about your new besom, @Dierna_Nimue_Selene! 
Willow is a lovely wood- it was recently the month of willow, as it is one of the Sacred Irish Trees 
I’m in the same boat as you are when it comes to walnut- I know the nut itself is associated with increased mental prowess and retaining memories (I remember because it literally looks like a brain 
). I flipped through a few of my books, and Jude’s Herbal Home Remedies by Llewelyn notes there are three kinds of walnut (white, black, and European) and says the following:
Skullcap and walnut have forms that resemble the shape of the human head, and can be used in treatment of headaches and nervous disorders (pg 6)
I can’t find anything about the tree itself though 
Although it looks like Jeannie found a great source with info for you- and from the info there, it sounds like a lovely wood to work with! 
Wishing you all the best with your crafting- blessed be!