In order to put your mind at ease, take a look at this very thorough and informative article on
identity theft. As you will see, the main purpose of identity theft is usually to commit financial fraud, i.e., run up credit in your name and then stick you with the bill.
If you think about it, that can't happen in China. No Chinese national can divert your credit card bills to their address in mainland China or issue a change of address card to the U.S. Post Office for the purpose of eventually stealing your credit card information.
Many Western people have this terrible fear that their passport information will be stolen and misused, but how is that possible? Can you imagine a Chinese national walking into the nearest American embassy with a digital copy of your passport asking for a replacement with the ultimate plan of entering the United States pretending to be you? Before having the guy arrested, I imagine a good hearty laugh would be enjoyed by all.
The most common abuse of Western credentials in China is in the improper handling of your digital degree: Chinese school owners will keep it, remove your name (perhaps the opposite of identity theft) and use it as a blank template for awarding degrees to Western applicants who don't have a degree. For this reason, I agree with Ken that adding a 50% opaque large diagonal watermark across the digital degree is a good idea. Tell the school owner or FAO that if you are hired, you will provide a clean copy.
You should NEVER send credit card information via e-mail or enter credit card information on websites that are not secured with SSL (where you see http
s:// in the url). When in mainland China, I never used my credit cards at hotels: always paid cash.