Another factor to consider is that
HPV+ cancer patients/survivors (oropharygeal or cervical) have demonstrated their inability to clear the
HPV infection without drama. In my son's case, both his parents proved themselves incompetant to clear the virus effectively - cervical carcinoma in situ for me, tonsil cancer for my husband, Genetics? Maybe, maybe not, but my young adult son has had his first two vaccinations with his third scheduled for this fall. I suggested the vaccinations, he did his own research and agreed.
Another factor to consider in public health issues that that vaccines (at whatever risk) protect the individual vaccinated and those the he/she comes in contect with. Vaccinating boys may protect them from oral cancer, and may also protect their partners, and their partner's partners down the road.
My best wishes, Ana, on your husbands treatment and on your decision regarding vaccinating your sons. Not an easily choice to make. You've probably got some time to think about it with your younger son, at least.