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Probably yes. USB cable i USB cable:) If you know how to attach it, you should be fine. My firend replaced many USB cables in many devices and everything worked fine.

The real problem is Micro-USB which is common in mobile devices. It has 5 pins and sometimes the additional pin is connected (with optional resistor) to +5, sometimes to GND (also with optional resistor):)

Normal USB shouldn't be a problem.

EDIT: some typos:)

teeny-weeny thingy?

USB connectors are pretty standard on the inside, so it should work. Just crack open your mouse (this will probably require removing the teflon pads on the bottom of the mouse and unscrewing whatever's behind them - keep in mind this probably might mean that you'll need new teflon pads) unplug the old cord, and plug in the new one, in the same orientation. Tada.