Well, the thing is, those control points are what actually determine the curve shape. While you could certainly have fewer points at the expense of perhaps less accuracy of the curve, you will never have none, and you probably need at least a dozen to maintain some semblance of the original shape.
The problem is likely with WoodWOP and its handling of splines. With a client of ours who runs the same software and called us with a similar problem, we were never able to find a satisfactory solution. WoodWOP apparently creates some sort of special point (it had a specific name, but I don’t remember what it’s called now) at EVERY control point on a spline.
You could try converting your spline into a series of more or less tangent arcs using the Convert command with output=arcs and a small angle tolerance, but IIRC, WoodWOP didn’t really care for that either…