Actually now that I think about it, the little bit of Japanese I have studied at university, the Japanese are all about “loanwords” which is basically they just use words from other languages and give it their own meaning. For example tape in Japanese is tape, but pronounced tapu. Though, it is not safe to assume they always carry the same meaning. For example Smartu in Japanese, doesn’t mean you are smart, it just means you dress fashionably. And Remember, its not Japanese if its not pronounced in japanese, despite country of origin. So I would imagine their word for astronaut is something like, Asutorunatsu. And since all words not of Japanese origin are written in Katakana, If my guess on pronunciation is right, then it would look like this.
アストルナツ
And I think it is safe to assume they would loan their word from english, just because it seems like half of their loan words are english, russian seems kind of rare from what I have studied thus far. so it wouldn’t be cosmonaut