so now I know that someone actually wrote a page about writing extensions for our website:https://inkscape.org/en/develop/extensions/
If you want to go that way, you should take a look there. The extensions you can consult for how to save the Inkscape file are, for example, the one called scour.py and there must be something in the gcodetools files, too.
If you only want to use wmf, that will be simple enough, because uniconvertor is used in other extensions, and you can just copy-paste.
Else (for emf) you might need to find a command line tool that can convert svg to emf, and make use of it in your extension.
This is probably what I would do:
You could also just write a script that watches over your image directories for changes, and if a file is changed, converts it to emf.
This would not require any extra extensions, or anything more than pressing Ctrl+S to save a file and update your wmfs at the same time.
There must be several examples in python and ruby available on the web, as django, pelican, jekyll and other web frameworks provide this kind of thing.
Only thing you need to find is something that converts svg to emf.