Never tried re-balling. The only facility I have for dealing with BGAs is at work (IR workstation) but it is U/S at the moment.
for small BGAs you don't need too much (and i assume that chip in the MP3 player is a small BGA package).
for small BGA packages you can get along with tin balls (from e-bay), tacky gel flux , IPA or other stuff to clean flux, fine tipped tweezers , steady hand and hot-air.
desolder the BGA with hot-air, clean the PCB and BGA with flux and solder wick, clean everything with IPA, apply flux to the bga, place the balls with tweezers, reflow the balls with hot air, clean up flux , apply fresh flux to PCB - place the BGA and reflow with hot air.
for bigger BGAs it won't work that way because of placing the balls with hand and incorrect heating with hot-air - you would need a stencil to place the balls and IR rework station to desolder/solder.