I figured out why Raiden was instantly skilled with the katana in Sons of Liberty.
I don't know if this was obvious to anyone else. I just thought about this right now and couldn't find anyone pointing this out online.
When I played Sons of Liberty, I found it weird that Raiden was skilled with the High Frequency Blade from the moment it's handed to him. I figured it was just video game logic.
Then I realized, the VR Missions expansion for MGS was his training. It's explained that this is where he learns most of his skills, running the simulations as Snake.
Well, there were three missions where you play as Grey Fox, using a katana.
Raiden mastered the katana through playing as Grey Fox in VR.
In the same way that the simulations gave him the skills of Solid Snake, they also gave him the skills of Grey Fox.