How does the application link up to the correct database then?
Normally that would be hardcoded in the application code. A parameter in the registry, ini file etc, or off the command line
Or there would be some mechanism within the application to choose the datasource to use.
Lets say it's hardcoded
e.g The application expects a DSN called MyAppServer to be pointing at one of the above.
Either thru a script or by writing little launcher application.
You'd wipe out MyAppServer, and then copy an existing DSN pointing at the chosen server and rename it as MyAppServer, and then run the application.
If you make the target DSN a parameter of the launching doodad, Then all you need is three shortcuts each one with a command line parameter of the name of the DSN you want to use.
If it's a registry or ini file then you just write a script to edit that.
Note if you are talking System DSNs, or ini files in privileged areas of the drive, or regsitry keys in protected areas, you could have access problems security wise. Some will be guaranteed UAC nags in Vista, if you are or want to use it.
DSNs are really really old tech, if you can get access to the source for your apps, I'd get rid of them and fix this issue as well.