The most obvious way to produce a PDF file from a .vss file would be to use MS Visio, the very same program that was used to save the .vss file in the first place. Alternative would be some utilities that support import of Visio formats, but given the fact how closed the format are, there won't be many.
Convert Microsoft Visio smartshapes data to Adobe Portable document format.
We have found 2 software records in our database eligible for .vss to .pdf file format conversion.
Microsoft Windows software - convert vss to pdf on Windows
A vector based diagramming software from Microsoft
Convert from vss file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned vss to pdf. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert vss to pdf on OS X
Microsoft Visio documents viewer for Mac