Follow this step if the wires are still connected. If they aren't, skip to the next step.

If the wiring to the circuit board seems fine, use a razor or wire strippers to clear the rubber insulation away from the USB.

Keep track of the colors! If you connect the wrong wires together, the speaker won't work, and you could ruin the board!

After removing the rubber insulation from the smaller wires, remove the access USB.

Splice in the new USB and wrap the connection with the colored wires in electrical tape.

If you end up with reduced sound quality, you may need to solder after all. Continue to the next step in that case.