Is it better for a woman to wear the niqab or to preach about Allah with her face uncovered?

A woman's covering her face from non-mahram (definition) men is obligatory, and it is not permissible to violate Sharia (definition) under the pretext of Dawah (inviting to Islam), for the end does not justify the means. Sheikh Ibn Baz was asked about a man who shaved his beard to be able to perform Dawah, and he replied that it is not permissible, and that if he cannot perform Dawah except by shaving it, he should move to another country, with knowledge and insight. As for a smile, it is a charity, and it can be a means of Dawah and influence in a way that does not violate Sharia. The outward appearance of righteousness from a Muslim is a good thing and can make him a role model, but a Muslim’s intention for people to see righteousness in him can be a cause for showing off (riya') and seeking reputation (sum'ah), which are among the things that nullify the reward of deeds.