Sorry, but we do not provide old versions of yEd for download.
Off the top of my head, the only "incompatibility" between yEd 3.16 GraphML files and yEd 3.19 GraphML files would be the elements from the SBGN palette section. Thus the simplest solution would be not using these elements for GraphML files that have to be parsed by your "old application". (You can hide the SBGN palette section to prevent accidental use of its elements - see "Edit" -> "Manage Palette").
Since GraphML is an XML format, another possibility would be creating a helper application that transforms GraphML files created by 3.19 into the GraphML format supported by your old application. As afar as I can tell, all this helper application would have to do is replacing SBGN elements with previously existing elements. Thus it might be possible to implement the required transformation using XSLT.
Finally, if none of the above is an option for you and you need this in a commercail context, you can contact the yWorks sales department to negotiate a custom agreement for access to old versions of yEd.