The Acrobat "convert colors" tool, in its "document colors" section, list the color spaces used by the document so probably a faster way to get this information?
Anyway, PDF-ShellTools doesn't have, currently, functionality to get this.
I also don't see in the Acrobat automation API's such functionality. Its Javascript API has a colorConvertPage method, that can be used to convert page object between color spaces, but I don't see any method to report the color space used by page objects.