Is it permissible to shun the hypocrite and the slanderer, limiting interaction with them to only greetings and brief conversation, and is this action correct?

It is permissible to boycott people who commit sins for the sake of a benefit, if that boycott leads to a positive outcome. Otherwise, the obligation is to consider the overall benefit and endeavor to win over the heart of the sinner. The Prophet, peace and blessings be upon him, boycotted the three who lagged behind after the establishment of the Islamic state in Medina, and his boycott had a significant effect on them. The forbidden boycott is that which is for personal desires, but if it is for a legitimate Sharia reason such as an innovation (bid'ah) or open defiance of God (fisq), or if it contains rectification for the religion of the boycotter or the boycotted, then it is not forbidden.