After neutering (or any surgery), I find it necessary to keep the cat safe. I really got the meaning of this when I released a cat back into his straw house after neutering. In about 3 seconds, he shot out of his house, across the yard, up a tree and across a nearby roof. He was out of his mind with anesthesia and stress.
From then on, I prefer to put the cat in a kennel over night. If the kennel is in a quiet place, the cat will sleep it off and be ready to be released where it was trapped in the morning.
Depending on your particular circumstances, keeping the animal safe may translate differently but that safety, freedom from cars and predators is necessary.
This is also a great time for me to show the feral what I am about. It's the closest to each other we have been. they will remember their night inside.
One of these cats pictured was doing poorly and required a medical exam and blood work. They're a pair so the partner went in for updated shots and exam. They spent the night in the kennel/spa after sedation and went back outside in the morning.
For neutering, I leave the male in the kennel over night. When the females are spayed, I keep them inside as long as they are willing. Up to three days if possible as their surgery is much more invasive. When they've had enough of the cage, they make it known.