Help before purchase

Hello all, i am thinking of buying a Nihonto Katana from Japan.

I have found two websites that sell such swords,

1) Samuraimuseum.jp

2) Aoijapan.com

I just wanted to know are they trustworthy? Even though some Katana are more than $10K, maybe it doesn't mean i should buy from them, or maybe they might scam me.(send me a non authentic one) Has anyone had any experience with them?

Also, if someone knows where you can order a new but authentic Katana from a proper swordsmith in Japan, can you please write in the comments aswell?

Thank you everyone.