Hank Reinhardt, co-founder of Museum Replicas, was on that video, and though he died in late 2007, the book he was working on is now coming out from Baen Books, titled The Book of Swords. Toni Weisskopf, his widow, took his various drafts and brought them together.
I was sent an ARC of this book, and have been looking it over for a couple of days...and I have to say, I'm impressed.
There are other books on the history of swords, but I haven't seen another one that so deftly combined the history of swords (around the world and through history) with the theory and practice of sword use, including the psychology of swordfighting. Most such books are written by scholars, not by someone who liked to take the sword (or a replica) outside and see what it could do...someone with an instinctive feel for the mindset of a warrior..and someone who had himself designed swords and then used them.
I was liking the book already when I found the two places where he describes his feelings on first handling two specific weapons...and realized how perfectly he described the feeling a very good (OK, extraordinary) sword gives the born warrior. (Yeah, I've had that feeling on occasion, as it's accessible to those with less ability and experience--but he had much more.)
His sources range from ancient texts through Icelandic sagas (I remember just enough of Njall's Saga to recognize incidents) to modern scholarly discussions and include his own long experience with edged weapons.
No matter what other books on swords you might have--and I have several myself--this one has a unique perspective that I think any serious fencer, swordfighter, or sword "nut" should buy as soon as it's available (October of this year.) There will be overlap on the history part--though informed by his wide knowledge and willingness to consider alternative explanations--but not on the swordfighting part. We are poorer for not having him around to learn even more from, but this book is a solid and worthy legacy.