If you install MATE Tweak (it will appear in the Control Center), there's an option under "Windows" to select the window manager (select "Compiz..."). You can also install fusion-icon to get this choice. Fusion-icon appears as "Compiz Fusion Icon" under Accessories in the main menu, and shows an icon in the upper-right app tray).
If you want to take it a step further and use the Emerald window decorator (install emerald, emerald-themes), choose "Select Window Decorator" in fusion-icon.