Generally, when removing parts without using hot air, damage to one part can be mitigated by sacrificing the other. For example, a damaged part is of no use, so carefully cutting it off, leaving just the pins on the PCB pads will ease the stress on the PCB - you simply wipe those pads clean, and use a solder sucker for any solder filled holes.
I'm not suggesting using wire cutters (which can easily tear off the pads), just that, you don't have to be overly gentle, you want to do the least damage/heating cycles to the PCB as possible. Constant heating and re-heating of the same area can cause pads/traces to permenantly lift, or through-holes/via to be pulled out. This can be a nightmare to repair with today's multilayered boards.
If you don't have temperature controlled hot air, then I would first cut any through-hole mounting lugs on the USB socket, then flood the USB pads with solder and flux so they can all be heated at the same time. Clean up with solder wick, and put the new one on.