USB is digital data, not analog audio. Without USB you might as well use your existing analog inputs (CD, tape). Does your MP3 player produce audio output?
Your board appears to be all-in-one. I can't recognize where left and right audio feed into the final amplifying IC. It may be within copper traces rather than wires.
Besides, if you solder your own wires to them, it's liable to introduce hum or other unwanted noise.
Then you must also find a way to disconnect other audio signals.
I believe such switching is already built into the unit via the CD & tape selectors? Or if these are in use then you can always add an external input selector.