Earlier I mentioned that the word 'Kumihimo' was modern, a search through Japanese archives, including the National Diet Library* in both Japanese (http://dl.ndl.go.jp/?__lang=ja) and English (http://dl.ndl.go.jp/?__lang=en) reveal that the oldest known use of the kanji for kumihimo is in an 1877 report (http://dl.ndl.go.jp/info:ndljp/pid/897375/21?viewMode.). This report is from a British Importer/Exporter, Doctor Dresser. The report shows the kanji in the table of contents section 14, wheat straw braids export available. Looking at the actual report page, the kanji only shows up in the title of the page on the left hand side, and within the phrase wheat straw braids. A translation of the page will be necessary for further study on the word usage though I'm confident that the objects referred to as wheat straw braids will not be items associated with what is now kumihimo but rather mundane items such as hats or sandals. The first hiragana usage of the word kumihimo at the National Diet Library is the 1929 Creative Design Collection, 2nd Edition. I've been unable to see the inside of this source but I suspect that this would be the first recorded use of the word kumihimo in association with the typical braids that we think of today.
With the earliest known dates, we now need to consider there timeline context. Now it is entirely possible and most likely probable that the kanji for kumihimo is older than 1877 but I suspect not by much. Let's take an overview of the timeline of kumihimo. What we do know is that the oldest known braiding book Itokumizu, for both kute-uchi and kumihimo, was written during the 17th Century. This book has no mention of kumihimo in kanji or hiragana; also telling is that the author does not name the loop braiding process nor the early beginnings of stand and bobbin braiding. The next two known books on braiding are Hiden Itokumi published approximately 1800, and Mano Ke Den Kojitsu Itokumi
Tetsuke written approximately 1818. And both of these books also fail to name the loop braiding and stand and bobbin braiding methods. These two books are unique in that they are considered to be a Master Braider's book with their patterns and thoughts and yet the word kumihimo isn't to be found.
Where I suspect the word kumihimo came from originated from the same place that words like rice paper and kimono came from; a simplification word to describe a whole category of objects that Westerners did want to learn the individual names of or grossly mistranslated. But as I've come to learn in this field, more research is needed.
* The National Diet Library is the Japanese version of the US Library of Congress.