it sounds like they are using a nonstandard coloring scheme. now i would think they replaced blue with white but i would highly suggest you cut apart the plug end and with your own eyes see which pins they wired the cables up to in order to make sure (and wire it up to the correct colors on the mouse cable.
once you figure out the direction/order the odd colors are wired on the plug you should be able to use the diagrams above to wire to the correct colors on the mouse cable.
assuming its a usb plug issue, that should fix it (assuming good soldered connection and wrapped in electrical tape. personally i'd use a diy usb end as its more clean but thats up to you. regardless since the colors dont *quite* match up with usb specs i'd check...