Where can I get a health certificate in Shaoxing without a business license?

You don't need anywhere. You don't need to apply for a business license in advance for a health certificate.

Health certificate refers to the proof of preventive health examination, which proves that the examinee has the health quality to engage in the prescribed business. Health certificate mainly involves six diseases in five industries, which largely protects the health of employees and clients. On June 1 day, 2009, China formally implemented the new Food Safety Law, and on July 20th, China issued the implementing regulations to allow hepatitis B virus carriers to engage in the food industry. Therefore, hepatitis B virus carriers can also legally apply for health certificates.

Physical examination place: local disease prevention and control center or medical and health institution approved by health administrative department to undertake preventive health examination. If this work is carried out without approval, the health supervision institution will not accept the physical examination form issued by it.