We tend to conflate three communications concepts that actually have very small overlap. We tend to speak of and treat "being a witness," "evangelizing," and "apologetics" as though they are synonyms. They are not synonyms, however.
"Evangelizing" is telling people what Jesus did for them.
"Witnessing" is telling people what Jesus did for you.
The difference is illustrated by Jesus meeting the Samaritan woman at the well. Jesus evangelized, then the woman ran to give witness.
The evangelist fills a specific office that not everyone is called to fill. The model in scripture (note: I said "model," not "law") is that an evangelist is called, gifted, trained, and then commissioned. The first two are done by the Holy Spirit, the second two are done by the Body of Christ. We see examples in scripture where all of these things are done, some very specifically. Apollos, for instance, who was obviously called and gifted by the Holy Spirit yet required training by Pricilla and Aquila, and we see later that he had been commissioned by the Church just as Paul had been.
But not everyone is called to be an evangelist.
OTOH, everyone is obligated to be a witness.
Being a witness takes no training in doctrine. It doesn't take any study to say, "I was lost but now I'm found." Notice than after Jesus evangelized to the Samaritan woman, she was able to be an effective witness after only a single conversation with the Lord.
Giving witness when the time arises is an obligation; in fact, it's a sin to fail to give witness. When Peter and John were commanded by the Sanhedrin never to speak of Jesus, they responded, "Judge for yourselves; how can we not speak of what we have seen and heard?" That challenge of "judge for yourselves" was made to the men who were the judges of Israel.
By what did the Sanhedrin judge? By the Law of Moses. What did the Law of Moses say? In Leviticus 5, it defines failing to witness of what one knows as a sin before God. So failing to give testimony to what Jesus has done for us in the moment such witness is called for is actually a sin, thus to be a witness is an obligation upon us all.
Both of these are different from apologetics. IMO, apologetics is more useful to believers with questions than to unbelievers. In fact, apologetics extended to unbelievers may be the primary example of "pearls before swine," in that it take basic belief (which is non-intellectual) to fully appreciate the apologetic appeal to the intellect. In other words, apologetics is a function of "equipping the saints." I would further assert that apologetics lies within the role of the congregation (which has the charge of "equipping the saints") rather than with evangelists.
What Paul--who had been trained in the intellectual approach--learned is that the Holy Spirit will have already "warmed the audience" to be ready for belief. Thus, the methodology of intellectual debate was actually a hindrance when the task was to evangelize.
However, for believers apologetics is very important, as we see it effectively applied in the letter to the Romans.
Jesus' advice was to go into all the world teaching people about the things that He taught us. So obviously, in order to do that, we need to KNOW SOMETHING. And Paul also said that we should study so we can learn to recognize Truth, so I wouldn't take the verse you quoted to mean that we should avoid knowledge of Bible teachings apart from John 3:16.
I've always believed the saying about the difference between an argument and debate, and that is that in a debate, people are listening to each other. I agree that arguing is unnecessary, and more often a waste of time, but debating is a good way to learn.
But the real question has to do with defining when someone is being a pig (or swine) that Jesus talked about, and also what it means to NOT cast our pearls before swine. I think someone can act like a pig well before they get to the arguing or debating stage.
