USPS seems to be fine to ship Li-Ion batteries installed in their devices internationally https://pe.usps.com/text/imm/immc1_014.htm#ep1059904 and there is nothing specific listed for Japan that would prevent it https://pe.usps.com/text/imm/il_010.htm#ep1628203
I was a bit surprised to read that one of the restrictions is that "Mailpieces must not bear markings or labels identifying the contents as lithium batteries."