I'm not sure that I can be all that helpful since - to my knowledge at least - my survivor has not experienced ASA and I gather that is what you are primarily asking about.
I can tell you how I reacted to learning about his CSA and how I think I might react if he were to disclose ASA. When my survivor first told me that he had been abused as a child I think my first reaction was shock followed immediately by sadness and anger. I felt rage that someone could have done this to him. I was never angry at him and I certainly never blamed him. I did not think he was less of a person. I felt closer to him for him having told me and I was glad that he trusted me enough to say something. I know very few of the CSA details, but I would certainly be there to listen if he wanted to tell me. I am sure it would make me incredibly sad to know the details, but I also think if he were to feel comfortable opening up about it, it would also bring us closer. I don't ask about it though because I don't want to trigger painful memories for him.
If my survivor were to tell me that he had experienced ASA I suspect I would react similarly to how I reacted to learning about his CSA. Shock, sadness, and anger at the perpetrator. It would certainly not change my feelings for him.
I don't know your personal situation and relationship with your sons very well, but it sounds like they love and care about you which leads me to believe that they would not turn their back on you if you were to tell them. I think sometimes it can be hard to keep everything inside and it can be good to have someone to share it with. Ultimately, the decision whether or not to tell them is yours and you have to do what you are comfortable with. I can tell you that I am someone who tends to lean on the strongly conservative side, but I also believe in loving people despite differences in beliefs and family is especially important. I suspect your sons will love you no matter what. I wish you the best in whatever you decide to do!