As I know that few our clients use MapWindows GIS to create shape files with success. You just need to save files using projection which is supported currently by RadMap (spherical Mercator with location set as latitude/longitude in degrees).
I'm sorry, we aren'e experienced in this particular tool. But I've found projection in this tool which seems like one is used by RadMap:
Category: Geographic Coordinate Systems
Name: WGS 1984
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