I'd like to hang a hook-arm off my desk's chrome wire rail to hold my
headphones. I do not want rounded S-hooks or J-hooks. I need a hook
with a level surface to hang stuff. Is there a hook less than $10
that's already made to fit such a rail? Is there hardware that would
allow me to rig an attachment to the rail myself? Thanks.

hook & rail example: https://i.imgur.com/BNZB54n.jpg

Check here for 2 or 3 possibilities, $8-$12, (skip past the J hooks)

https://www.shelving.com/Wire-Shelvi...ries-s/218.htm

Thanks for your reply. The $9.99 Accessory Hook (SI-ASMKH6C) is just
what I'm looking for and it's the same one going for $15.04+shipping on
Amazon. Unfortunately the website won't divulge the shipping cost
without filling out their purchase form first. For now, I'm more
inclined to buy the $11.46 Amazon J-hooks (https://rb.gy/woe56v). I can
always add to the purchase to qualify for their free shipping. However,
I still think the straight hook arm is more convenient for hanging
headphones.