Nice photo. Cool crank.

Certainly a skip-tooth crank etc would be consistent with a 1937 date on an American bike; but a normal 1/2" chain is also common on American bikes of that period. More to the point: what were Japanese chains like at that period? I don't know, but I'd guess they were the same as English ones, typically 1/2".

I agree with those who say the bike just doesn't look that old. It's too clean, the paint is too even; the paint on such an old bike will have faded in some places, remaining dark in others; dirt will have accumulated in the nooks and crannies; and so on. Of course it's possible for a bike to have been in storage the whole time and not got that kind of aging; but the odds are against it. And the plastic thingie on the right crank arm is definitely not that old.