Not a shinai, a type a bokken / bokuto. The links above got the look right. See http://bokkenshop.com/eng/245.html
. But using the school names is a bit of a problem. Each school used something just a little bit different making it difficult to get it right and making the term more or less meaningless for everyday use outside of that school. I just want to know the name for the two broad categories straight swords and curved swords. Perhaps those terms are the best that I can do.
For the record, my straight sword is a Kiyota standard issue. Living as I do a dozen or so blocks from the place I don't have a catalog. I suppose I could go there and ask, but I can never get out of the place without an hour's worth of conversation.