I think it is something to be a bit careful with. I'd have thought paint for children's toys would be ok, but best to read the label. It would need to be water based. In the Uk you can get water based plastikote waterproofing paint for wood, that comes in different colours, which is what most people on here use on wood items in the cage.
I don't know if it would be available in Tokyo though. Is Mark's Tokyo edge based in Tokyo?! It's a stationery shop that sells plastikote apparently.
Anyway this is the stuff
https://www.amazon.co.uk/Plastikote-...5R00FW1AX6C39J