My question is this: “Is there New Testament evidence we should we be speaking more about truth, and less about “believing” or “beliefs”, when we speak to non-believers?”
I found all these citations where the apostles said they spoke truth, or implied they spoke it, and then they remarked about creating or not creating belief. They never appeared to use “belief” for persuasive effect, only as an observed result.
Scripture Citations of Support
Acts 17:11 Now the Berean Jews were of more noble character than those in Thessalonica, for they received the message with great eagerness and examined the Scriptures every day to see if what Paul said was true.  As a result, many of them believed, as did also a number of prominent Greek women and many Greek men.
Acts 13:12 When the proconsul saw what had happened, he believed, for he was amazed at the teaching about the Lord.