I believe DirectX is a mesh format, so you may have better luck going the SolidWorks to STL to X route. An STL to X converter may be easier to find.
Check at the Sycode site. They have loads of mesh converters.
I was heading down that path when I downloaded quick3d pro. I was unsuccessful loading a STL file in that, but I didn't try too hard yet. Now that I know STL and X are related, I'll try harder. I'll also try your suggestion for the converter.