Can Cayman company documents be apostilled for use abroad?

Yes. The Cayman Islands are covered by the Hague Apostille Convention through the United Kingdom, so apostilled Cayman documents are accepted in other member countries without consular legalisation. Banks, lenders and foreign registries often ask for an apostilled certificate of incorporation and a recent certificate of good standing.

Certification and apostille

Source: Status table: Convention abolishing the requirement of legalisation for foreign public documents, Hague Conference on Private International Law (HCCH)