I have this odd Targus laptop bag (https://www.targus.com/us/productdeta...x?sku=TSB110US) that includes hideaway backpack straps and rings to slip on a shoulder strap. Used mini-carbiners with the shoulder strap rings to attach to the rack, and the backpack rings at the bottom to loop a mini bungee around. Yay.

Right now I am attaching the bungee to the axel with a small chain link. That tiny bit of pressure shouldn't hurt the axel right?

No Problemo. Looks good.

You can bolt a small J-hook at the end of the rack stay, down there at the dropout. Then hook your bungee on that.