Wait a minute. I wonder why the adapter is marked with 125 V. USA is 120 V and Japan is 100 V. Maybe it's rated for 125 V to account for tolerances. (120 V actually means 114 V and below 126 V.) But under normal conditions, your wall socket will give you a lower voltage than that transformer is rated for. This is just a regular transformer (not a switching power supply) so the output will vary with the input. If the tranformer was designed for 125 V and you give it 120 V, the output voltage will actually be 4% lower than the normal output voltage. This won't damage anything but maybe the battery won't be fully charged. My guess is that 125 V is just overprovisioning, though.
I'm also unsure what "So I've got a few that are straight 125V, but one of them says 125~V." means. ~ in this case wouldn't mean "approximately" but AC. Even if the ~ is missing on the other packs, it's all the same, just different markings.