How to detect the profile for a CMYK PDF

[hankr]

As a follow up to this long thread, the simple question wasn't answered:

How can one determine the correct ICC profile to use on a PDF that is in the CMYK colorspace, when I have no other information? Can you get an embedded profile, and reapply it to use as the base when converting to sRGB.icc?

identify -verbose on a PDF does not give any details of the profile like a tiff.

Technically, I'm using MagickWand, but i would assume the solution would be similar regardless.