well i know that noone really used the straight-bladed "thing", but in Masaaki Hatsumi's Ninjutsu History and Tradition, i see a shinobigatana that looks mysteriously like a regular kodachi with a daitou's saya... is that all it is, or am i missing something?
nope. it would be the one on the tatami with the massive sageo... in the section labeled "shinobigatana" or something to that effect. although i lost my book and am running on memory, so the details are probably a bit off.
Page 94 in Ninjutsu History and Tradition shows a picture of a "Shinobi Tanto" on a tatami mat and a "Ninja ken" on the floor/rug. Edit: Just giving a page number and captions of the pictures, I can't actually answer your question.