Is it legal to carry a genuine tamahagane katana in Japan?

Question:

I was wondering, once you register the sword and everything, if you can openly wear it with a wakizashi like the samurai did

Answer:

It's illegal to carry any possible weapon without any reasonable due reasons.
This regulation could be applied even for kitchen knives and wooden sticks.
No matter if it's registered or not.
What is the "possible weapons"? What is the "due reasons"? That's police can make a decision on site and the court would judge later.
If police considered it's possible weapons, you could be arrested.

If you were learning " i ai do" ( a sort of martial art in which you use a real sword), and it's on your way to the training class of "i ai do". You might not be arrested. You need to prove that fact.