oh, Lucy, I am so, so sorry. It is so hard to let them go. I think you are making the right decision, it would be heartbreaking to inadvertently cause him more pain by not taking any action. :grouphug
I had my vet come to my house to help Sydney Sue cross over. It was beautiful. I have a very small house, and all the other dogs (two other greyhounds, and one Chinese Crested) were in the living room with us. I did crate the crested, because he was super high energy, and I didn't want him messing with Syd. When the vet came into the house, Syd went and laid down on her bed, like she knew. He gave her the injections, and when she was gone, he listened for a heart beat, and told me she was gone. I went into my bedroom (to cry and bawl and sob) and my best friend and the vet wrapped Syd up and took her away. The vet took her to the crematorium, and I was sent the ashes a week later. There is NO way I could have been in the room when he wrapped her up. But letting her go at home was just so peaceful for her, I am so glad I did that for her.