Shipper is simply a person (or company) who contracts with the carrier for carrying the goods from one place to the other. So in your case, if your company has (or will) contract with the carrier (Ship or aircraft) for carrying these goods from China to India, then you will be the shipper for this consignment and your company's details will be in the bill of lading as the shipper.

Consignee is the person (or company) for whom the goods are meant to be. In your case as the goods are meant to be for your customer in India, they will be the consignee in the bill of Lading.This article could be of some more help on this topic. "Shipper, Consignee and Notify party explained" 

Regarding custom clearance, I do not see any problem in this provided the rules are followed.