Actually, once I had worked out how best to do it, they really didn't take very long at all. Probably a couple of minutes each. I managed to get beech strip, 5mm by 10mm from a modelmaking store online, and I used a coping saw, a very sharp chisel, a soft pencil and a piece of sandpaper.
I didn't have access to a dowel plate, so I roughed out the shafts, and then very gently pressed them into the key, which gave a guide to how much there was left to take off. You need to leave them a bit big, so that they fit tight into the hole in the key. It is vital to support the key as this is done, otherwise it could break.
The original tangents supplied with the instrument were 2mm by 10mm, and because they were so narrow, they had a tendency to move from side to side. The extra width has provided a step above the shaft that rests on the key itself and provides support.
It has to be said that they are not quite as finished as they appear in the photograph, I didn't see the need to polish the parts that don't contact either string or key! However, it has been the main cause of improvement in the sound of what was a cheaply made hurdy-gurdy, and it has given me confidence to do more.
Note the nut, which was a single piece of ebony. I have split it into two, and used another piece of the beech strip to create a partition. Because they have been made quite tight in each side, they can be adjusted without using anything else to hold them in place.
I played it in public for the first time yesterday at the Shroppie Fly in Audlem, and it behaved quite well, considering all the strings that are on it I found in instrument bags and workshop drawers. Now I have made it work, I think it is time for a new set.