The latest I know of UniGraphics is that it uses the Parsolid kernel. As such, saving your part/assy as a Parasolid (*.x_t or *.x_b) is your best choice. Though other solid formats will work (ACIS=*.SAT or the STEP formats) since both SWX and UG use Parasolid that is your best bet. IGES is the format I have seen the most problems with so I would recommend avoiding it.
You will not be able to save your SWX file as a parametric UG file. Some programs can open another program's native file. I have not had the need for a while, but a few years ago I did have occasion to open several Pro/E files in SWX with good success. If you are really lucky the guy with UG will be able to open your SWX file, but I would not bank on it. He should not, however, have any trouble opening a dumb solid sent to him in a Parasolid format.
- - -Updraft