I’m from California and used my blue parking badge permit as “proof” for the handful of discounts I got. I will admit I had no idea I could do that until midway through the trip, when an employee at the Toji Temple gate suggested it and asked if I had some sort of verification. I expect that should be fine to use for other places.

As far as I see it on the website, it looks fairly accessible. They have wheelchair rental service, too.
https://kagoshima-barrierfree.com/barrier-furee/%E7%9F%A5%E8%A6%A7%E7%89%B9%E6%94%BB%E5%B9%B3%E5%92%8C%E4%BC%9A%E9%A4%A8/

When I took my daughter to Japan earlier this year we used her blue badge parking permit (UK government issue) with generally positive results. It’s got her name and photo on it and it is in multiple languages. I think Australia has something similar.

Rented mobility scooter at Tokyo Disney. It’s slow, 3km is max speed which is a crawl. Wondered why I didn’t see anyone using the scooter but it did allow me to have a seat to rest when there weren’t seats available.