You're unlikely to be able to get the drive to work with a USB to Parallel converter because they are intended for use with printers - they present the computer with a USB printer and relay the data from it to the parallel printer attached to the converter.
An ExpressCard parallel port should work, in theory, depending on how IOmega wrote the drivers for the Zip drive. If they go through the Windows parallel port driver layer then, as long as the ExpressCard behaves exactly like a traditional parallel port at the hardware level, the drive should work. If the Zip drivers bypass the Windows parallel port layer and attempt to access the port directly, you're more likely to have problems. The ExpressCard port will appear as a PCI parallel port rather than as a traditional ISA port on the old 0x378/0x278/0x3BC address which the drivers may be expecting if they attempt to access it directly.
I've never used a PCI parallel port (even my Socket AM3+ motherboard has a pin header on the board to allow a parallel port to be connected which is then available on the traditional address - that may change next time I upgrade, though...) but I've heard that their level of compatibility with "real" ports can vary when they're used for things other than printers (which is probably all the manufacturers test them with).
In case the ExpressCard port allows you to configure its capabilities, the interface chip used in the Zip100 drive uses EPP (Enhanced Parallel Port) mode if possible; if the port doesn't support this, it will fall back to PS/2 (bidirectional) mode then, presumably, nibble (standard/compatibility/AT) mode. It can't use ECP (Enhanced Capabilities Port) mode; in my experience, it doesn't seem to like ECP/EPP combined mode either.
I've heard that USB to "Real IEEE1284 Parallel Port" converters do exist, based on the USS720 chip, but I've never used one and I don't know whether they would work with the Zip drive in Windows - they would be subject to the same compatibility conditions I outlined above (and probably be even more strict about how the Zip driver is written).
If all else fails, you may be able to find a cheap USB Zip drive on eBay.