Your cnc/laser should accept NURBS data and cut that.. This will be correct curves only limited if you machine is making straight lines instead of true curves and then that resolution is controlled at the machine controller/CAM software. This would be the iges, sat, step, 3dm exports. STL data is polygons and only "looks" curved if they are small enough... For the 3d printing, the "facets" will be visible if they are big. The smaller you make them, the less noticable. If you dont want to see them, then mesh the facets very small in the stl output dialoue

Here is a sphere being meshed at a low polycount



Here I set the divide larger thasn value to .1



This would make all the little facets be .1 at it's largest.. This would be hard to see on a 3d print of a sphere. You can make them smaller.