I can't find any stand-alone copiers like those you mention, nor any floppy disk controller cards for PCI slots. That leads us to having an older computer / mobo that does have a 2-floppy controller and cabling included, and using it to build a computer whose main purpose is dealing with both old floppy formats. The computer would not have to be very modern or powerful for this. For example, I still have a couple older units with 500 MHz Pentium2-class or 1.2 GHz Pentium-3 class CPU's, and less than 1 GB of SDRAM. The older one even has both floppy drive sizes, just like you need, and it's running Win XP Pro.
If you do this, try to stock up on a few old floppy drives - they are getting real hard to find in working condition. ALSO make...