I made that decision twice with cats. One had cancer, and although it sounds awful, I can't remember about the other one after all this time, just that it was terminal.
My experience with vets and end of life was so gentle and kind. The one cat was the loveliest companion I ever had and I was allowed to hold him, to cuddle him, which he clearly wanted, as the vet gave him his injection. The other cat had a different temperament, wanting to play and be skittish, and the vet found she was calmer without me in the room.
Love to you, DD, and to Benji.