Yes! Got it to work!
Well, admittedly, I found a different but quite obvious solution: I used the firmware zip Kobo Desktop downloaded (murg mentioned the path
here), copied the contents over to the .kobo directory and - voilą! - the KT updated cleanly. The only thing I had to do though, was to remove all my books I had copied using 1.9.17 before and to copy them over with Calibre again, otherwise opening a book would lead to a crash.
Whatever, so far, everything works like charm, it seems to be more speedy and responsive and some mistakes I had with books before (like ignored dropcaps at chapter beginnings) are gone!