Since the concept of a "fundamentalist Baptist" is built on a foundation of strawmen and if full of so much baloney to put it nicely, to describe a catagory of telling the Good News to others is kind of a moot point.
The whole premise of fundys is that they are seperate and holy. They claim they are the true independent local church, apart from say the SBC, which they claim is a denomination. Nothing could be further from the truth. The SBC is not a denomination, but a confederation of local, autonomous churches. The entire concept of fundamentalism is a false one. Lots of religious groups are built on false premises, such as the RCC, Latter Day Saints, and JWs.
They claim they are the only group to put Jesus and the Bible first, which is a false witness within itself. This is exactly what other Baptists, such as the SBC do, as do many Protestant groups.
Telling others the Good News is telling someone exactly what the Bible says. Nothing needs to be added to it, such as a third grade brat approach with a chip on the messenger's shoulders. One can tell of the consequences of dying without Jesus without screaming it in their face. Just because a person does not always act angry, does not mean it is a watered down message like Joel Olsteen delivers.
Fundamentalism, as it exists today, does nothing, absolutely nothing to bring praise and honor to the Lord.