Thanks so much to all who contributed suggestions for this dodgy handrail fitting. Here is how we solved
1. We found another Beneteau
owner and worked out the solution was to stick a tiny screwdriver or drill bit into the hold on the shank. Then use this as a lever to make the shank turn. That unscrewed from the round piece going around the rail. The shanks on the friend's boat were a bit easier to undo than ours and it helped us to establish which direction we should unscrew in. Once unscrewed, the fitting slid off the handrail. We took the whole handrail off ie unscrewed the other two fittings as well.
2. We used a jig saw with a very small narrow fitting to cut a groove into the top of the broken screw stuck in the hole, then removed it with a screwdriver.
3. We took the broken screw and the fitting to the nearest welding shop and had them welded back together.
4. Re-installed the handrail - good as new. No need to buy a new fitting.