At my company, we set the mins to the approach we're using to back up the visual. One of the reasons, I assume is that if ATC switches us to an instrument approach at the last minute, there's one less thing to do. Everything's already set up.
On a related note, why is it that non-US carriers seem so hesitant to accept visual approaches? If you've planned an ILS to a runway, and ATC offers a visual, it's pretty rare to hear a non-US crew accept the clearance. Just my unscientific observation.