Yes, probably wise to let a Thai attorney handle filing of the application for probate and subsequent orders allowing you to distribute the funds per the provisions of the Will. And would recommend you get a quote from the attorney as to the cost. I was told by the CM attorney who drafted my Thai Will that the probate would take 5-6 months to complete and the attorney fee would be around 60,000 baht.
If the Will is in Thai, you're all set; if not, a certified translation will be required. As executor, you'll be responsible for paying the last expenses (medical, funeral) costs for the Decedent from the estate funds (or, perhaps, you'll be reimbursed later for paying before the reimbursement is authorized by the local probate court).
Upon his death, you'll need to get a release from the hospital (which basically means expenses have been paid) and a release from the Decedent's Embassy/Consulate. Both of those are required before you'll be able to retrieve the body from a morgue.
If Decedent is a US citizen, cops and/or hospital will notify the US Consulate of the death and Consulate personnel will start the "looking for kin" process.....which you should promptly head off by visiting the Consulate and showing them the Decedent's Will. I don't know Embassy/Consulate procedures for other nationals.