The MX Chip uses a coin cell. One side of the coin cell is positive (labeled with a +), and the other side isn't labeled at all (this would be the ground/minus - side):
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I'm pretty sure the Wii uses 2032s like this one ^
It may be difficult to get the solder to stick to this, so I would advise scraping it a decent amount where you plan to solder to it. This helps the solder to stick better.
Also, like any other battery, you don't want to heat it for longer than you have to. Some coin cells vary, and I know of an instance where one exploded. Having said that though, these cells aren't too scary when they explode. 18650s or 21700s are the ones you REALLY don't want blowing up on you.