Using Firefox (which has this configuration option) doesn’t work? Or using a extension for Chrome or other approach to force all links to open in a new window?
This would not apply to Android/iOS tablet users… any fiddly approaches to pop up a ‘window’ would not be supported in Android/iOS devices and they fallback to effectively just opening a new tab as they do now. (This is where something like Fully Kiosk browser is so beloved on Android devices as it provides a UI for this use case.) So it would only be for desktop users who don’t use a browser that supports opening links in a new tab or similar alternative… 
I suspect that’s more a limitation of the browser. With Firefox, when I had it configured to open links in a New Window, even if I had SharpTools full screen, the new window would open in a small view layered on top of things, so it was easy to close (video below).
Have you looked to see if there are other ‘Kiosk’ type browsers for Windows? Or even tab / kiosk extensions for your browser?