I thought you might say that :). According to the docs, this is all supported by default on Azure.
The trick here is to still have 'app.wsgi' in the URL, but make it invisible to the user. To do this you'll want to use the
URL Rewriter. I don't have the exact syntax (nor a Windows machine to check) handy, but what you'll need to do is create a rule that changes
while excluding static files (i.e., add conditions to the rule to exclude /images or /media or whatever from being rewritten). The important thing is that the URL rewriter runs before IIS chooses the handler, so that app requests will go to app.wsgi and
the static requests (which aren't rewritten) will go to IIS for speedy handling. Also, the client will never see the second URL - only IIS will.
You might have to change your routing code, since the path will now be in PATH_INFO.
Your app will still generate the URLs you want the client to see, but if for whatever reason a URL escapes with app.wsgi in it, I set up a rule so that http://example.com/app.wsgi/App/1/sh001/ac001/po001 will 301 redirect to http://example.com/App/1/sh001/ac001/po001
(for SEO and all that fun stuff).
I'm pretty sure the URL rewriter module has templates for both of these rules to make it a little easier for you.