I know I am very late to this party, but I think alpine Linux is the OS you are searching, I only used it in docker but it is indeed very small. (Only half a gig or something) also if something has a USB Port but not much disk space maybe use a live usb-stick distro like tails (also quite practical when you don’t want to be spied on). Hope that helps with a future project.
A distro building in top of Arch for Pentesting aka. Hacker-Arch