E.H.
Oh my goodness I am so sorry you are going through this. We have a dog and know we may have to make this decision in the future.
I would include you son. Many may disagree with me. But here is my reason why. Lies traumatize our children. True we don't have give all the details but enough so that when the child starts to grow and something triggers the memory that will say mama thought enough of me to tell me the truth. Even if you have to do it while he is out of town, make sure to tell him the truth as a 4 year old can understand, "like all dogs go to heaven" if you believe in that.
I just saw a show last night where a young boy was diagnosed with a condition of eating things like clothes, dirt, paper, etc.(I know this is off topic but just follow me...lol) Well, she took the son to the doctor and demanded that the FIX him. Well, the poor child thought he was a freak! Guess what? The doctor finds the Mom in the bathroom of the child's hospital room eating toilet tissue. So she lied and never told the son she had the same condition. When the son found out she had lied all of his life you can imagine how that made him feel. Then the doctor treating the little boy shared with him the lie his mother told that affected him since he was a little boy, who learned of his mom lie, he told the little boy he never forgave his mom and to please find it in is heart to forgive him mom. So! I said all that to say, please be honest with him, don't have him wondering all these years and wondering also if he can ever trust his mom or anyone for that matter.
Sorry so long!