Aizatulin

You can use smooth and turn off "constrained boundary" option. If you do, you can additionally set a constrained point group, which keeps the position. You probably want the "side points" with the sharp corners not in this group.

If you want to group procedurally and you have a grid like geometry, you can straighten it and use the relative (uv)positions to group the borders or you just manually group the points. If you don't want this group keep just keep it empty of course or turn it off (check attachment).

Here is an example for a revolved surface using VEX.

I think it is quite hard here to get good results. I've done experiments by setting weights on each point, which is used as weight to influence the voronoi pattern. So the default weight should be 1 for every point, which should give you the standard voronoi pattern.
My first idea was to influence the distance by the weight. Just calculate the distance between every point and each target point and divide it by the weight. If every weight is 1 the result is equal, but if you set even one to something different, you will lose the convexity and the new pattern will look very different.
The same for the second idea, which is more a faked voronoi using booleans. For each cell and for each point pair you can apply a boolean by intersecting a half-space (giat cube), where one side is inside and the other is not. The plane psoition can be inluenced by the weight ratio for each point pair. The problem here is similar to the first idea, because you will lose the convexity and the pattern looks broken.
The third idea is influence each point based on the weight of the neighbours, where the neighbour can be defined, but I would take the adjacent cell for the original vornoi. This will give a voronoi pattern, but the neighbour cells are also inlfuenced. And it is hard to avoid this becauce the neighbour relation can change during the process.

I'm pretty sure there are many more approaches, but you can look into file if you want