What is a suitable simple, open web server for Windows?

As others have stated, Apache is the clear choice here: flexible, well-tested on Windows (any "NT" version of Windows), for your application will require minimal configuration changes. Small footprint too. While Apache has rightly been criticized for a glut of configuration files, for simply dishing up some files, you would literally have to make one, maybe two changes to the default configuration:

Listen <your new port> and potentially: DocumentRoot c:\my\binary\path

Another aspect that you may not have considered is the binary signature and anti-virus: httpd.exe is a very common process, well-documented, open source; will not trigger false positives like perhaps a lesser known "freeware" Windows web server (Symantec uses it for their Endpoint Protection product to do exactly what you're doing: distributing update binaries to clients; I would think if it works for Symantec...).

Also, there's a built-in service install, all scriptable from the httpd executable (httpd -k install -n "MyServiceName" -f "c:\files\my.conf") so easy to "sidechain" from the parent installer. Easy to clean up/uninstall (again, httpd -k uninstall -n "MyServiceName").

More information here.

There is Apache for Windows. I'm not sure how IIS would work, as it depends on licensing and your situation.

Is there anything else that appears when Googling for "windows free web server"?

Why not IIS with WebDAV enabled? Seems simple, and included with the OS?

http://learn.iis.net/page.aspx/350/installing-and-configuring-webdav-on-iis/

Apache? It's (I believe) still the most popular webserver around. And there's a windows version too, with a .msi installer, and works as a service.