Exporting any of the Visio graphics (including .VSX) to PDF format is likely only possible with the original Microsoft Visio, or any other dedicated Visio viewing with PDF export support. This seems like the only viable choice.
Convert Microsoft Visio stencil XML file to Adobe Portable document format.
We found 2 software records in the database related to .vsx to .pdf file format conversion.
Microsoft Windows software - convert vsx to pdf on Windows
A vector based diagramming software from Microsoft
Convert from vsx 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 vsx 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 vsx to pdf on OS X
Microsoft Visio documents viewer for Mac