Articles about this never talk about the impact of moving your common keyboard shortcuts. Being physically unable to use Ctrl-S,Z,C,V with my left hand while using the mouse with my right would be difficult to retrain around.
I've found that using X11's highlight + middle-click paste has drastically reduced just about all of my reliance on using shortcuts for copy/paste, at least in any application that requires me to keep my hand on the mouse (like a browser) rather than keeping both hands on the keyboard (like Vim).
I've been using Dvorak for ~10 years, but primarily with the command line or other non-mouse driven interfaces. However, at work I'm condemned to a life of Windows, Office and Visual Studio. One trick I've found is to keep both Qwerty and Dvorak installed. When I want to use Ctrl-S,Z,C,V while also using the mouse I can just do "ctrl-shift ctrl-[SZXCV] ctrl-shift". The ctrl-shift action is quick enough that I barely notice it anymore. This is also useful when using other applications where remapping the keyboard would become tedious or isn't possible. It helps that I'm not too slow with Qwerty so there's no hunt&peck when I switch layouts.