Dear Ms. Latona:
Sorry to hear about your cancer. Without seeing the results of the various tests, it is almost impossible to tell you the chances of gaining a stronger voice. With peripheral nerves there is always hope for nerve regeneration. Much of the possibilities would rest on what type of insult the nerve underwent. If it was surgical then the chances may be modestly better than if the damage was due to the malignacy (invasive damage of the cancer). The best guess is that your larygneal nerve on the left should get better, but how much I cannot say. I would ask your surgeon.
The posterior arytenoid muscles give the voice depth (if I remember my medical school anatomy).
Peripheral nerves usually have the theoretical chance of regeneration for up to 18 - 20 months or so. However, remember if they have been destroyed then there is no hope of regeneration. It does sound like your nerve damage was peripheral to the cell body, which is good.
Sorry, I just have no idea about your chances. I do think you will get a stronger voice over time, but how much I can not tell you.
Sincerely,
CCF Neuro MD