Connections to replace Public Info in Global Search

We're implementing Redwood, but don't quite feel ready to start using Connections. I've been able to figure out some customizations to get around sticking with My Team, but I can't figure out how to 'turn off' the ability for users to click on an employee's name in the Global Search field and access their Public Info. Looking for suggestions on that and/or how, when we move to Connections, that Public Info is replaced by it. My expectation would be that Public Info would be completely gone, but for testing, I did enable Connections and disable Public Info, and I was