The Mikawa quake was the only quake in WW2 Japan to be censored, and it left a very large subsidence circle on the bay floor near three islands (though the Image was poor quality) which intersects the fault line that apparently moved as a result of the quake. It was apparently at eleven kilometres deep but a significant strata subsidence suggests a circular event of perhaps a kilometre at most. A coal mine/deposit beneath the bay could have been used and the carbon would have absorbed the betaparticles.
There is no evidence Japan had any kind of nuclear capability in early 1945.
Even if they did, conducting an underground test would have been the least useful way to get information about it. Getting information from underground tests is much harder than above-ground ones.
Nuclear weapons of the WWII variety would not have set off magnitude 6 earthquakes anyway. While underground nuclear tests can set off small aftershocks and even create fault lines, there has never been a major earthquake attributed to a nuclear test.
In short, I think you are grasping at a lot of straws here. You have no positive evidence for such a thing — that is a bad way to approach a research topic, and leads just to conspiracy mongering and evidence "of the gaps" (hypotheticals not yet ruled out by evidence). It is a bad methodology. To put it another way, you might as well be asking whether aliens induced the earthquake, with the evidence you've got.