Too bad Japan doesn't have nuclear weapon
No, but the USFJ does, I guarantee you. I mean, the entire fucking 7th Fleet of the United States Navy was transported - and that's just ONE element.
Now, officially, all nuclear weapons of the United States military were removed from Japanese soil back in 1972. Officially, anyways.
...After that, the Cold War was still in high gear. And it's been pointed out that, technically, if you have nuclear weapons on a ship... It's
technically not on "Japanese soil." And that's what the United States Navy did after 1972. Now, "officially," there's no nuclear weapons on surface vessels and only SSBNs have nuclear weapons. Officially.
But then again, USS Ronald Reagan - CVN-76, was transported as part of the 7th Fleet. A legit capital supercarrier. With aircraft that can deploy nuclear weapons on its deck.
Now United States Navy policy and official word is absolutely no nuclear weapons are on board carriers. But... I guarantee you my left arm that somewhere in the USFJ or the fleet that there's some sort of nuclear weapon. Whether on the SSNs (and since the story takes place in 2015, they had up to three SSNs in Japan with the 7th, not just the one that is there today), the Blue Ridge or the Reagan... There's a nuclear weapon somewhere. I doubt it's actually on Japanese soil, but there is one somewhere. You don't have a fleet and military force that large in such a dangerous region (read: Thanks China) without having something nuclear to throw in desperate scenarios.
TL;DR version:
Yes, there's nukes. But they're in the hands of the United States Forces Japan/American military that were isekai'd alongside with Japan.