What should I look out for when importing lithium-ion batteries?

It is difficult to make risk-free shipments for the battery of the products. But you can minimize the risk. The most effective way is to start working with a reliable battery cell in your product. This will solve most of your problems.
Moreover, pay attention to work with a factory which has enough equipment to test batteries. Not only outlook and function check but also a comprehensive life cycle and safety test with a strict AQL. Make sure that their incoming quality control team is doing the process regularly for each lot. Ask your factory to provide these IQC reports to you. If you have a chance, go and check in person, or do it via a 3rd party company.
Besides this, in the outgoing inspection process, you can repeat these life cycle and safety tests based on an agreed sampling qty. This will help you to verify that the IQC of the factory is doing their job.
Another suggestion, please make sure that your batteries have date codes on it and do not let your factory to use more than 3 months old battery. Considering the production and transportation time, when your customer receives the products, your battery will be probably 6 months old already. Usually the brands give 6 months guarantee to the end customer to replace their batteries which in total accumulates to 1 year from the production of the battery to the customers' 6 months usage time. This is usually the warranty that the battery suppliers.
There are also proven design requirements for the batteries. If needed, I would like to help with further information.

Regards,
Mert.