What little I can find in terms of info:
1) 26 pin floppy is for laptops. They like small connectors and thin cabling
for such things.
2) 26 pin and 34 pin (desktop) floppy signal names are similar sounding.
It looks like the 26 pin cable might support one drive, but I can't guarantee
they're similar enough to "roll your own" cabling. (In other words, they
could use less signals on the cable, by removing things like support for
two floppy drives on the same cable.)
3) I can see a female 26 pin to male 34 pin adapter board. Not likely to help you.
It implies though, that by selecting the right signals, you could make one work.
You'd be better off looking for a 26 pin micro floppy drive for a laptop,
which would be a replacement part, then see if the seller also has a
26 pin to 26 pin cable to go with it. Rather than, starting with that 34 pin
floppy drive you currently own, and try to find a 26 pin to 34 pin cable to
allow using the desktop floppy. If you stick with a scheme which uses a "26 pin
on each end" style cable, it might be easier to whip together.
This is an example of a cable - perhaps you can compare the look of the
connector here, to what you've got on the motherboard ? It looks like
it might have a 26x1 slim on the end. I've also seen people selling
ordinary IDC 0.1" connectors in 2x13 format, for a 26 pin floppy interface,
as well as some elastomer 26 pin connectors, so you'll have to be
just a little bit careful while shopping. Plenty of crap out there.
And with the quality of the available pictures, it's really hard to
say just what's on the end of the cables.
https://microdream.co.uk/media/catalog/product//i/m/img_0612.jpg
Purely a guess,
Paul