I'm so sorry for your situation. I lost my very best friend and sidekick, a 14 year old Dalmatian named Pongo, on December 6th. I had to make the decision but my vet made it easier by telling me he thought it was time. He had a heart murmur, and like you, I hoped he would pass in his sleep and keep me from the pain of making the choice. His heart was big and he was a love bug so I knew he wouldn't want me to be alone after he left. I applied (and am waiting to bring her home) for my first greyhound. I see him in all his special places here but I know that he isn't in pain and I did the right thing. But I miss him so much. You will too. But give her relief from her pain. He was cremated and sits by my front door, where I tell him to guard the house just like I always did when I go out. It's comforting to have him with me.
