I had my animals killed at home when it was possible, simply as it meant less stress for them. Normally I kept out of the way, but one time I sensed the slaughterman wanted me to stay and watch and and I am pleased I did.
Chasing and catching an animal unless completely tame is a stressful thing for it, but it has to be done for welfare purposes, such as checking its thriving, looking for fly strike, hoof maintenance, shearing, lots of things, and each time its caught it is just as stressful. The final time it wont know its any different than those other times, and the stun gun is incredibly quick.
We know what is going to happen, and catching them all those other times we say, don't be silly I am only trying to help, so that last time will be no worse, and as long as your animals have as good a quality of life as you can give them, that is the best you can do unless you intend to become a vegan
My first two pigs caused my much stress both before and after, probably as I had allowed them to become too much of pets, after that, though they had the same fuss tickling and attention, I tried to make sure they did not become individuals for me, and it made it a bit easier, though if they had to go the the abattoir I always booked them in for first kill and took them to the pens myself. And not one of them ever looked stressed.