Is there another reason John had for stopping Sarah?
Does he need another reason? As John says to the T-800:
I don't care!! There's gotta be another way. Haven't you learned anything?! Haven't you figured out why you can't kill people?
Look, maybe you don't care if you live or die. But everybody's not like that! Okay?! We have feelings. We hurt. We're afraid. You gotta learn this stuff, man, I'm not kidding. It's important.
This is the key theme of Terminator 2: It's not okay to go around killing people just because it's convenient.(1) This belief is what separates the heroes from Skynet. The theme manifests in a number of ways throughout the film.
The scene immediately before John and the T-800 arrive at Dyson's house is a turning point for Sarah Connor. She was traumatised by the events of the first film. She fears and hates the Terminator above all else, but has also chosen to become the Terminator. Like the Terminator in the first film, she tries to kill her enemy's "parent" so that her enemy can never exist.
When Sarah reaches Dyson's house and
chooses to lower her gun, even though Dyson is injured and helpless on the floor in front of her
this is a crucially important decision for her character. At the last moment, she rediscovers her humanity and her capacity for mercy.
Before John decided to go after Sarah, the plan was for him and the T-800 to leave Enrique's compound and cross the border into Mexico. It would be logical for John to lie low, hide from the T-1000, and wait for Judgment Day so he can fulfil his destiny as leader of the resistance and eventually destroy Skynet.
However, John refuses to go down this path. Instead, at great personal risk, he goes to stop Sarah and then
destroy the Cyberdyne facility.
John does this because he believes trying to save three billion lives is better than allowing the war to happen, even if the latter course will result in his victory over Skynet.
(1) It says something about the moral universe of Hollywood action films that it seems weird, even incomprehensible, for a protagonist to believe such a thing.