Button activated popup into incognito browsing

Hey, I am making a domestic violence resource site, and I am looking for popups that when you click a link or button, it opens up your browser page incognito.
The idea is that, the client want's an escape page for DV user to press if their abusive partner were to take their phones or look through their partner's internet browsing. If something like this exist as a plug in or if there is a code for this, that would be freaking great!