I am very sorry you are going through this. I really think though that you need to get over the idea that it is "selfish" to allow him to keep feeling sick and not take any action in any way to either ease or end his suffering. Keeping him alive because you don't want to have to make the decision is what is selfish. Selfish is thinking of what you want for yourself instead of what is best for him.
At his age, with the weight loss and other signs, the most likely possibility is that he has some form of cancer. Even if you spend the money to run all the diagnostics and find out that that is what it is, will you be able to treat it? Do you think it is in his best interest to continue this way? Do you really think you'll be able to give him the good quality of life that he deserves?
There are many ways to explain to kids that a pet is very ill, very old, and most likely going to die soon. There are many ways to deal with the loss and honor their memory. However, if euthanasia is chosen, I don't think it's necessary to try to explain that to very young kids - it can take him in to be euthanized, and you can explain that you took him to the vet to try to see what they can do, but unfortunately, he was just too sick and he ended up dying there. It's really not a lie - just a simpler explanation. I would save the euthanasia talk for kids that are older and will have an easier time understanding why it was necessary.
Again, I am very sorry for what you are going through. He's given you a lifetime of love and companionship, and now is the time to return at love with the best gift you can give him at this point. He wants to go, he just needs you to help him get there. (((HUGS)))