Borderless windowed mode is a pain with floating windows and no cursor lock

I only have one monitor, so I like to use floating windows to watch videos while playing games. Borderless mode is required for this.

Unlike a lot of FPS games however, the cursor isn't locked to the center of the screen during gameplay, so often when moving around frantically my mouse manages to hover above and click on the floating windows. This basically tabs me out of the game, leaving me helpless to enemies.

Please lock the cursor to the center of the screen during gameplay, or add the option to do so in the menu.