Have you had the best scan possible? I don't know enough on that topic, but others will and hopefully they will post.
I will right the rest of this post assuming that no other scan can find your cancer.
How long will you be on HT? If the answer is less than a year I wouldn't be too worried about osteoporosis. I note you are 78 and it is true recovering from bone loss is difficult after your 50s, but I don't think you will lose much in a short time on HT. All the side effects vary from person to person, you may get none or one or two, or all of them. HT will help the RT work so I think it is worth trying. HT is most significant started a few months before RT and for the few months after.
If I were in your position I would accept the first three month shot of HT and see how well you can tolerate it, and then take the next shot if all was OK. I would probably not stay on it longer than a year.
If this treatment does not cure your cancer, the next option will be HT for life, so it is worth giving this the best chance of working.
If you do end up in the position of HT for life, consider asking to delay that until the PSA is in the very high hundreds, it may take several years to get there and when you do start HT it can knock your PSA to near zero, and then it can take many years before it returns.