A heat pump that is ~1x1in won't freeze (or even get that cold) moving only ~2w .
A USB port is spec-ed for 5v@500mA or 2.5w.
Don't bother as that TEC is already too weak.
That might be more than Vmax and burn it out. Don't know specs of the TEC used.
Qmax = 25.7W
Vmax = 15.4
Can you measure your TEC's dimensions and or remove/replace it easily?
Even if you can't I think you could have a great time making your own little cooler...
A 25 W TEC, a piece of 2" diameter copper piping with a cap soldered or even AS5 + taped together, some mounting pressure and an old heat sink from the scrap bin. Insulate that bad boy and you are ready to go
Man, I wish I had a full work shop... can't wait to get to school and have access to all of the tools I need...
Keep us updated on the hacking