Those programs you mention are not ment to be used for games. The models you want in a game should be made out of polygons. Solid works makes solids, just as other CAD programs like Inventor and 123D Design. I am not familiar with neither Catia or NX however if they aren’t polygon modeling software, they won’t simply make the right kind of 3d objects. As for Meshlabs and other ways of converting these models to the other, theres no way of doing so, without any errors. Your outcome model often involves polygons and vertices colliding. For example if you model something as simple as a cube in Solidworks and tries to make it a polygon model, you won’t get one face per face if that makes sense. Instead of making a cube inside of solid works and then converting it you would rather make a primitive or sometimes called simple object inside for example 3ds max. For more complex objects the struggle is just getting worse if you would try to convert models.
You mentioned Blender as an alternative program. I’ve heard it’s supposed to be quite simple to learn but since I don’t know what kind of objects your going to make I can’t recommend you none other than 3ds Max since that’s what I use. But for a start you might look around the different workspaces Max, Maya, Blender and other programs have to give you and idea what you are looking for.
I hope you find my answer somewhat useful.
Best regards - Joakim