His ancestry is never revealed in UHF, though it can be inferred by his teaching a karate class. Though, Japanese does have an 'r' sound, rendering the "Supplies!" gag meaningless.
You know, when I saw this movie as a kid, I honestly never even thought "race", I thought the idea was just that he was supposed to be some crazy fucker. It never once occured to me it was meant as LOL AZNS and I don't think it was.
