@valhenry2012 ,
Hello and Welcome to Mayo Clinic Connect.
I am so sorry to hear that your husband has such a burden to carry, and you along with him!
It must be frightening and uncertain knowing he's got not just one issue, but another as well.

This is a link from the Head and Neck Cancer group you may find helpful.
And one of our esteemed Mentors, Don @dsh33782 is familiar with head and neck cancer, as he is a surviver of it...plus more!
https://connect.mayoclinic.org/comment/773041/
You ask a great question about how his treatment may affect his HCM...
but we can't answer that here. That's a question best left to his treating physician along with his cardiologist working together. No two people are the same, so it would be impossible to state with certainty.

Are you comfortable with his cardiologist and their expertise in treating HCM?
Are you near, or have you considered going to a Center of Excellence (COE) for treatment in this complicated case?
When does he start treatment?

@valhenry2012, apologies for the late reply. I'm glad @karukgirl was able to direct you to the Head & Neck Cancer support group here: https://connect.mayoclinic.org/group/head-neck-cancer/

I also want to tell you about a specialty called cardio-oncology. Heart issues can be a concern with some treatment options. You may ask about a cardio-oncology specialist or department where your husband is receiving cancer care.

Mayo Clinic offers a program to address heart problems associated with cancer treatment called cardio-oncology or for people who have a pre-existing heart condition when diagnosed with cancer. The Cardio-Oncology Clinic (https://www.mayoclinic.org/departments-centers/cardio-oncology-clinic/overview/ovc-20442193) evaluates people prior to cancer treatment and patients who have experienced side effects due their treatment, and can help evaluate treatment when you have both cancer and heart conditions.