In KDE you can make a window borderless. There should be a way to do it in Cinnamon too, I guess.

You know what might work?

You could try using Xfwm4 with Cinnamon, and getting a theme that does not contain a title bar.

Example: Border Only XFWM4 theme

This theme displays nothing but a 2px border.

There’s very likely a simpler method that doesn’t require changing the window manager, but it certainly is an option.