I decided to build this as an adapter for a micro-usb cable, rather than build a standalone cable. I like the idea of possibly leaving it attached to the GPS, and it might be nice to be able to change out the cable easily. I think it will make for a more portable and attractive final result, too.
Electrically, this is very simple. The GPS already has a USB chipset built in, so it’s just a matter of matching up pins.