Custom Content Type with no MIME type?

Sorta a weird thing here: is there a way to have a MODx resource that has NO content type? What I want is the script on the page (i.e. a Snippet) to dynamically determine which content type to use, then print the appropriate headers. This is a download page, so it might have to be used to cough up a download of a .doc, a .pdf, or an .xls file -- each of those content types uses its own custom MIME type.

Normally, I'd just create a static file for this, but it's arguably a bit more secure to lock down this download page because it's intended for use only by logged in users.

You can't save a new content type without specifying a MIME type, so that doesn't bode well for housing this script inside of MODx.

There is a context-wide setting: set_header=0 but this would play havoc on the permissions. MODX does not write the headers until modResponse has parsed the output... so maybe I can tinker with that somehow?