Then call the AppleCare number for your country or call a local Apple retailer.
I'm not sure I quite understand the part about sending it to get fixed here in the US. What did you lose? If you sent it in to be fixed then it must be possible to fix it. Probably I just don't understand what you are trying to communicate. My apologies.
Considering the cost for a new current gen shuffle, I don't think it will be an economical repair. That USB connector is connected to a very thin ribbon cable that runs up the shuffle inside the case. If its USB connector came off and is lost, that means the ribbon cable got torn off. So the shuffle will need to be disassembled and a new part (USB connector with its ribbon cable) installed. And that's significant labor.
However, if you are good at fixing small things
I've done it before. You'll need to acquire a broken iPod shuffle 1st gen, but one that has a working USB connector. That's the most common failure for these iPods, so make sure it is described as being recognized by the computer/iTunes or something like, "It works but the battery is dead."