Without a file it's hard to say, but is it possible that the part is in fact not a solid? Your selection filters are set to entire assy and solid, which would prevent selecting face-only bodies.
For any customers who use non-native imported geometry for CAM programming, I always recommend using the Optimize Face command for cleaning the geometry up. This usually takes care of most geometry related problems.
If you want to keep the original geometry unchanged, then create a copy of it using WAVE Geometry Linker or Extract Geometry. Then use the Optimize Face command on the copied part.
Use the default settings in Optimize Face. They are usually good enough to clean your part. Try this and see if you can select the body in workpiece afterward.
igs is surfaces only. As you mentioned, you can save as stp, and you will have a solid if there is a solid in the file. You can use the igs too, just make sure the appropriate selection filters are used. Glad to hear you sorted out the problem.
You do have the ability to get a Solidworks part directly into NX without having to export a Step or IGES file. There is no Solidworks option when you use File-->Import, but if you simply use File-->Open you can change the Files of Type to a .sldprt file extension and open the Solidworks part for a direct translation.
Note that opening solidworks files directly is not an option included in all the bundles. You may need to buy an additional license to access this functionality.