Yep, the Mark I is right for the old AWs. I have an order for 3 of them from ebikestop.com right now. It's somewhat worthwhile to stock up, since if you crash and the bicycle hits the ground on the right side, it usually immediately mangles the indicator chain where it protrudes from the hub. Many vendors charge outrageous prices for indicator chains, however.
I don't like the look of the new black plastic shifters, so I got a N.O.S. vintage one on eBay for about the same price for my own 3-speed.
You'll also need a cable routing system...I suppose that you could route the cable through housing all the way down, but the way it's done on my bike has the bare cable going through a pulley system for most of its journey from the handlebars. You might have some of the hardware still on the frame. It consists of a plastic "fulcrum sleeve" (cable stop) mounted in a special clip on the down tube and a pulley assembly down near the bottom bracket. I've seen other bikes use the same technology but route the cable along the top tube with the pulley near the seat cluster. The fulcrum sleeves tend to shatter with age, so it might be hard to get a good one off a donor bike.
I heart AW hubs.