Yes, marriage certificate produced by Cayman Islands Registrar Office is valid in some of the nations in the United Kingdom. In Asian countries, you will have to follow the rules and regulations that is applicable in the respective nations.
If you have lost, misplaced or never received this document for your Cayman Islands wedding, email them and they will arrange to have it applied for, collected, and mailed to you. The cost of this service is $30 if you were married by Simply Weddings, and $50 if they have to do a search because it was another Marriage Officer.
More details will be provided to you by http://www.cayman-islands-weddings.com/about-simply-weddings/what-to-do-with-your-registered-marriage-certificate/ who are experts in wedding ceremonies held in Grand Cayman. May you couple live together a long way!