I think you'll find Tohei taught his own bokken work. How anyone can believe a Japanese of that era in the martial world didn;t have some and probably lots of sword training is beyond me. I need no books to tell me that.
What if Tohei himself told you that? He was never coy about it, he really had no formal sword training - although he often taught with a bokuto. He even wrote it down, in "Ki no Kakuritsu".
That doesn't mean that what he was doing was bad (or good), but the assumption that anyone Japanese must have sword training is...mistaken, IMO.