I'd use the debug preprocessor:
#if DEBUG
'Your connection string
#else
'Live connection string
#endif
Personally, I would simulate a live environment as much as possible to avoid situations like this. This means working as if the application is deployed. With the method described above, you wouldn't care if it's on your local machine or not, you just have to remember to build your app as "Release' instead of "Debug" when pushing it live.
Doing something just because it's easier to debug will make your life more difficult down the road.