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 sure you get floppy disk drive cleaning kits for both sizes. I have found that, by far, the most damaging thing that destroys floppy diskettes and ruins their data is dirt on the heads of the drive that gouges marks into the diskette surface. So, since I use floppies infrequently, I am in the habit automatically of cleaning the floppy drive and letting it dry out before ever inserting the diskette and trying to read. If you can't get a 5.25" floppy cleaning kit (hard to find, I'm sure!), you may have to resort to periodically opening up the drive and cleaning manually with a Q-tip and rubbing alcohol.
Two ways to work, then, with such a machine:
1. Machine has both 3.5" and 5.25" floppy drives working as A: and B:, and you just copy between. You might even put this machine on a network and make its floppy drive resources shared and available on the network.
2. Machine has only one 5.25" floppy drive internally, plus USB ports to which you attach an external 3.5" floppy drive unit.