Hey there.
Would you consider adding a content type field to the file objects in the success callback in the Dropbox JS Chooser?
This isn't currently available in the Dropbox Chooser, and I can't say if or when it might be, but I'll be sure to pass this along as a feature request!
One thing you may want to do is maintain a mapping of file extension to type and use that against the returned file extension. For example, we have a list of groupings here:
https://www.dropbox.com/developers/reference/developer-guide
Just adding on here: if we provided a "content type," we would do so just by mapping file extensions to MIME types (e.g. ".txt" means "text/plain"). So you may as well do that mapping yourself.