It's sad, but sounds like you're doing the right thing. Big hug.
For most vets AFAIK it is standard procedure to do the two-shot version (sedative then the shot that actually stops the heart). The only two times I've seen it done otherwise were a) with a very frail dehydrated cat where they had SO VERY much trouble getting a vein that they didn't want to fool around, just did the actual euthanasia straight off, she was for sure 'ready to go' and it seemed peaceful; and b) my first cat, in heart failure, being done on a weekend evening in the vet's home workshop on an emergency basis, and for whatever reason he offered me the choice of 2 vs 1 shot, and I said to skip the sedative as the cat was fairly out of it at the time, but I guess because of his enlarged heart it took multiple *large* injections of the euthanizing agent before it worked, and he struggled and seemed upset, and I will never again elect to skip the sedative.
I would think, for a basically-healthy animal, you would really want the sedative first, it doesn't add that much to the cost and either will make no difference or will make it easier for the animal.
Big hug,
Pat