Get a hose clip big enough to fit round the layshaft, put the spring in place and slide the hose clip over it. The clip needs to be just tight enough to be a tight slidding fit on the shaft. Now you will find it easy to push the balls into the ends of the spring. Then push the sliding dog up until it is contacting the clip and then use a couple of screw drivers to lever the balls in against the spring whilst you press on the balls with the screw drivers. It still requires a bit of dexterity but the hose clip keeps the balls contained and gives you something to lever against with the screw driver. Doing it all inside a carrier bag is an idea to, it saves having to search the dark recesses of the shed when they fly out
Anyway, take a look at this chaps attempts and you won't feel so bad. He has over 20 video's on Utube and is riddled with bad engineering practice and ignorance....but the first part of this one is hilarious
https://www.youtube.com/watch?v=NkG6Z-hXln0