Sorry this reply is late in coming, but I don't get by here too much anymore.
That being said, I've never heard of Shintaro Katsu having any actual sword training. Stage swordsmanship has always been standard training for acting schools in Japan, since back in the Edo period. Movie sword fighting is quite a bit different than actual Japanese sword arts because the basic idea behind it is totally different.

While several koryu sword schools have occasion to use the reverse grip, it is very rare and highly situational. It is very rare because it extremely limits your movements.