I’ve had to do this 4 times myself over the years, you most definitely want to be there for your dog, he would be there for you, it’s stressful enough for them to go to the vet. It’s a straight forward deal once the IV is in, they inject a sleeping drug which acts really fast, then the heart stopping drug, in my experiences it’s a peaceful process that is over in less than a minute. Don’t drag this out if he is suffering, put him to rest, best of luck.