You might be better off to load the connection string into some runtime variable and use that as the source for your connections. Load it from the web.config as the default, change it if necessary based on a user choice and store it somewhere it can be used by all database connection objects.
Most of my sites use a base page class that all pages derive from for the purpose of providing access to commonly used values and utilities. That's where I'd put it personally, but you may not use that model.
-Peter
compiledthoughts.com