How to pass / send a pre-designed .docx file to a printer to be printed , without open MS Word,by Java using either native libraries or other free 3rd party libraries.
Use Apache POI to open the document, extract the information you want and print it yourself using the Java Print API. Unless you're processing known documents this will be exceedingly difficult.
Use Microsoft Word through COM (this may meet your requirement, since no Word window needs to actually open, it'll run in the background), open the document and print it. This will require use of the Java COM Bridge which has some nasty native requirements and would require Windows.