This one of those things where you really have to see a specialist. It could be everything from Parkinson's to something very minor. I wouldn't want to even speculate. He really needs to go to a medical facility to have this properly looked at.
Thanks for writing to the forum!
A hoarseness persisting beyond two weeks needs an evaluation by an ENT specialist. It could be due to varied causes like upper respiratory tract infection like laryngitis or pharyingitis, head and neck cancer, oral cancer, reflux laryngitis in people who have acidity and GERD, muscle abnormality, voice box abnormality, polyps, tumors or weakness of voice box etc.
Hope this helps. Please let me know if there is any thing else and do keep me posted. Take care!