Don't kill
It was a matter of fact that, from now on, no matter who he met, a part of him would always wonder if the other person was a system user. But excessive suspicion was not only really bad for him, it would actually distract him from locating actual system users since his attention would be spread so thin.
What he needed to do was, keeping in mind everything he knew about systems, maintain a vigilant state for clues. Only if a person behaves oddly or did something out of the ordinary would he consider analyzing the likelihood of them having a system. Maybe this way he would miss out on actual system users, but the fact of the matter was that he had other objectives than just looking for system users, and if he didn't ration his mental capacity, he would fail in all his tasks.