You have received so much good advice already. What you said above REALLY resonated with me though. When Scarlett was diagnosed, and I had to let her go, I felt like I was killing my best friend. Unlike you, I had already lost many pets over the years as I grew up breeding and showing poodles. It sucks in every possible way. There is no getting past that. The only difference was that they had all died in puppyhood or as adults. I had never had to make the decision to let one go. Letting Scarlett go tore me up more than deciding to take my grandmother off life support and I absolutely adored my grandmother so that decision was heartrending. It took me a very, very, very long time to accept and understand that I had to speak for Scarlett and that I was not, in fact, killing my best friend. Neither are you. You are choosing to make the most difficult, but ultimately the kindest and most loving decision you can make for Sherman. It is going to take you a while to believe that but please do believe it.
The sad truth is that you will handle this, you will find your way through it, you have no choice. We are all here for you. You can cry to us when you don't want Sherman to see you sad. You can know that we have, almost all of us, been where you are right now.
Kiss Sherman, make memories with him, take pictures of him. All of that will stay with you forever.