I'm pretty sure none of Apple's portable devices can handle 24-bit/96KHz playback. 24/48? No problem on my iPod touch, iPhone, and iPad.
However, 24/96 is something my Mac can handle. Like you, I have an iPod classic in some drawer.
You are best to refer to the iPod specifications. I've never seen Apple claim that 96KHz playback was possible on any of their portable devices.