Shouldn't be a problem

How large will the package be?

In China, the postal office might check the goods and charge a fee. But if the quantity (and size) is small enough, it shouldn't be a problem.

The US customs will charge different tarrif on different type of goods(such as textile vs. glasses). That also depends on what type of the goods you declare(Gift, Mechandise, Sample).

There are Im/Export companies in China. But for a "testing water" start, it's not worthwhile to go through them.