I had that issue, too.
workaround:
You could make a var in a script tag in the index html before loading cordova and let that var store the unchanged file object. Then declare that var in your typescript definitions and use it.
//index.html
<script>
var VanillaFile = File;
</script>
// the cordova js import has to be after that
//declarations.d.ts
declare class VanillaFile extends File {}