You didn't mention what USB standard the equipment is using. If it's very old at all, it's likely using USB 2.0. USB-C was designed for USB 3.1 and beyond. It is backwards compatible, in that, you could get an adapter to plug a USB-A/B device into a USB-C port, but the opposite is not true; hence the lack of USB-C female to USB-B male cables.
USB 2.0 A/B cords used 4 (sometimes 5) wires (image courtesy of Wikipedia). Micro and mini cords are the same pins in a smaller form factor.
On the other hand, USB-C has ... a lot ... more pins (image courtesy of Wikipedia).
But notice, it still has the standard V+, GND, and Data+/- lines, so you could make your own cables by splicing a USB-C extension cord like this from amazon and a standard USB A/B cable to fit into your device, but it is not guaranteed to work correctly. Of course, this cable would be like an extended port coming out of your device - not ideal.
If your devices use USB 3.0, then they have the updated "Super Speed" ports which do have pore pins as well (image courtesy of Wikipedia).
As you mentioned, USB 3.0 B - C male-male cables do exist (on Amazon). You could theoretically cut off the USB-C male end and splice in a USB-C female end from the above extension cord. Again, it's not guaranteed to work.
If you want to add a true USB-C port, you could get a breakout like this and solder jumpers from the correct pads on the breakout to the pads where your current USB port is soldered to the board (after you remove it), or to a cut and stripped USB-B wire going into your current USB port.