>shear the image_map towards the cone axis so that it is not distorted
upon
mapping.?<

Well, that would be a distortion now, wouldn't it? :-)
Anyway, isn't the cylinderical mapping projected from the axis outward?
In that case, it will work on both cylinders and cones, and anything
that is radially symmetrical(is that the right term?) around that axis.
Of course, the image will appear stretched out of shape...but with
objects like cones, even UV mapping won't help.

>Anyway, can conical mapping be achieved by means of uv-mapping a
simple linear_spline lathe?<

Why not UV-map a cone?

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