How do I do this against a non appearing refund from a Thai hotel 4 weeks waiting for? Do I sent a letter to the hotel (no longer answering emails) with all the details asking for chargeback, or do I ask the credit card company to do it?

If you have copies of the cancellation, hotel terms and subsequent emails then go directly to the bank and say that the merchant (Hotel) is no longer responding to your messages. Demand an immediate charge back.