I think the best thing to do is to interop with word.  The idea is to launch
word, shove your rtf into it, tell word to print, and tell word to quit
without saving, and do all this without creating any windows.  There are
examples of this in the documentation.  FYI, I had mixed success with this a
couple of years ago, the rqt was dropped, so I didn't pursue it.  My problem
was in making word quit quietly under all curcumstances, and I don't recall
the details.