The Total Remote is a "consumer IR" device, i.e., a replacement for remote controls for TVs, VCRs, etc. Communication is one-way, and very slow. Not suitable for hooking up the iPod as a peripheral.
IrDA is rather like Bluetooth: it replaces cables between devices, and requires hardware/software on both ends for the devices to establish a connection and communicate. The ipod probably doesn't have this, and IrDA is still very slow for disk drive purposes even if it did.
Since it also supports Firewire, the ipod might have the hardware and firmware needed to drive a USB-to-IrDA adapter, but it's very unlikely: the USB standards folks have developed something called "USB On-the-go" that's more peer-to-peer-ish like Firewire, but almost everything on the market is still built around the original "PC master, device slave" protocol.
Buying a USB host adapter for the Z is almost certainly the cheapest, and mybe even the only, off-the-shelf option for what you want to do.
Ran