Has his voice completely gone? Or is it just reduced to a whisper? If he can still manage to whisper I'm guessing that this is due to inflammatory changes from the radiation, the resultant oedema of all the tissues in his throat/neck, and will improve as healing takes place . Have you discussed this with his RO?
In the meantime he could use the Speakit app on IPad to help with communication.
Tammy

Caregiver/advocate to Husband Kris age 59@ diagnosis
DX Dec '10 SCC BOT T4aN2bM0 HPV+ve.Cisplatin x3 35 IMRT.
PET 6/11 clear.
R) level 2-4 neck dissection 8/1/11 to remove residual node - necrotic with NED
Feb '12 Ca back.. 3/8/12 total glossectomy/laryngectomy/bilat neck dissection/partial pharyngectomy etc. clear margins. All nodes negative for disease. PEG in.
March 2017 - 5 years disease free. Woohoo!