I am really saddened by this news. Nobody likes to lose a best friend and constant companion, but neither does one wish to see such a loving creature suffer.
I genuinely wish you and your family the very best in this difficult time, and I know your four-legged pal is going to miss you you as well, but he'll be in a better place for sure, free of suffering.
I've owned a number of pets over the years and this is really the only part of pet ownership (and quite frankly, I think it's really the pets who own *us*) that I disliked. Somehow I never minded having to wash a urine-soaked cat (terrified of enclosed spaces -- e.g. the carrier), but making that final visit to the vet was something I all too often had to leave to a family member a little less attached than I because I just could not bear to do it myself.
Fortunately, in time, only the happiest of memories stay with us.
Please take care, and if you need to lean on anyone in difficult times, there are plenty of us here for you to lean on.