Years ago I visited Doc Price's forge down in Plymouth as part of a BB hammer-in. I got to see some of his collection of Japanese style swords. He did a bit of mixing on some, forging them from Wootz that he made himself.
Calling things hand forged might be read a couple of different ways. Most sword smiths (and many bladesmiths in general) use some form of press and/or power hammer. The blades are still refined with hand held hammers, but the grunt work of drawing out is done with help.
Defining traditionally made is going to remain vague. I doubt that it would be insisted that its only traditional if forged from tamahagane, but can well imagine that forging would be required.
A slight change of subject, but if you want a bit of a mind blowing look at sword making, you need to look at Kyle Royer's Excelsior project on Youtube.