It depends on if you are talking about the later Quaife complete gearboxes, or the earlier Quaife gearsets that were fitted to AMC boxes. I have never seen any mention of a provision for kick starters on the complete Quaife boxes (5-speed and 6-speed), and their catalogs never mentioned that option. I've had a couple of them, one 5-speed, which I still have fitted to a MK3, and one 6-speed, since sold to a racer. I don't see how they could be converted to kick start without a lot of effort.
For the gearsets fitted to the AMC box, as kommando and SteveA have mentioned, you need the road version first gear, which has the internal ratchet teeth to accept the kick starter pawl. The 5-speed that came in my PR had that gearset fitted, and after breaking two of the first gears kick starting the bike, I swapped over to the racing first gear, which is solid, with no internal ratchet teeth. The design of the road first gear weakens it seriously, compared to the solid race first gear.
You mention that there is no kick start shaft. Is there still a hole for it in the outer cover, either welded up or with a plug?
So, in summary, if you have the complete Quaife gearbox, you're probably out of luck. If you have the AMC box with Quaife gearset, and it still has the inner and outer cover with the kickstart provisions, All you have to do is find the appropriat first gear pair. Good luck with that. They are pretty thin on the ground lately.
And, as SteveA pointed out, if you have an outer cover with no provision for the kick start shaft, you might also have one of the sets with a ball bearing in the inner cover and a smaller layshaft end. Quaife did make a 5-speed gearset in that configuration, and it can be fitted into a Commando AMC shell with a little machining. I had one with that gearset and a plug to seal the hole for the kick start shaft.
And to add to the confusion, Quaife also made a reinforced gearbox shell, as well as inner and outer covers in the Manx style, with no kick start provision, that could be used with gearsets made for the AMC box. It all adds up to a lot of configurations you might find for Quaife gearboxes for Nortons. Not to mention the final Quaife design gearbox with a drum shifter mechanism.
If you search this forum for Quaife, you will find some other posts with more details on the various Quaife configurations.
Here are some pictures that might help (or might not).
Picture of the later complete Quaife gearbox, but prior to the drum shifter unit.
This is a picture, courtesy of Kenny Cummings, of one of them with the outer cover removed. Note the different clutch release mechanism and the ball bearing for the layshaft. I don't see an easy way to convert this to kick start, but I wouldn't say it's impossible. Might be able with combination of Quaife and AMC parts, and significant machine work.
For contrast, this is a 5-speed with Commando inner and outer covers on a Quaife shell, showing the kick start hole in the outer cover plugged. The inner cover was modified to either add a bushing for the Commando style layshaft, or a ball bearing for the Manx style layshaft. I've done both, but no longer remember which one this was. And before someone asks, no, I also don't recall what the two holes around the shaft plug were for. It's been a long time since I did this stuff.
A poor quality picture of the road first gear, showing the internal ratchet teeth for the kick start pawl. The race gear was solid on this side.
The two differernt layshaft styles, Commando for bronze bushing, and Manx for ball gearing.
Ken