I would say tread carefully but go ahead and tread. My husband found his birthmother in his forties and it was a positive experience for him. Your father may have lost touch with your mother and then realised too late that he wanted to know you. He may be happy to hear from you and welcome knowing you.
I think you have a right to ask him what happened, and why he chose not to be a part of your life. But be prepared -- he may or may not have a satisfying answer. "I was a dickhead and still am" may be the closest approximation of the truth. But "I was a dickhead and I regret it keenly" is a possibility too.
If you are a naturally curious person, and he is in his eighties, you may regret hesitating until it was too late. I would send a letter, give your contact details, and then suggest coming to his house at a certain time on a certain day. If he doesn't want to see you he will at least have to reach out to cancel. And at least your appearance at the door won't come as a shock.
I don't think you need to worry about the feelings of any other family members he may have. Unless he is Rod Stewart, his children will be middle aged and perfectly able to cope with this, and you have no particular responsibility to them anyway. But you could just say in your letter that you are doing your family tree and thought he might be related to you, so that if someone else reads it first it isn't immediately apparent that you are his long-lost child. He will know, of course, but you won't have outed him. That's what the parent-finder who found my husband's birth mother did - she sent a letter just asking if the lady was related to my husband.
Good luck!