There's actually a much easier way to change the connection string.
Go to the Settings screen, where the connection string is displayed as a connection string.
First mark and copy the connection string that's displayed.
Then change the type from connection string to string. The text for the string will change to include xml.
Then paste the copied connection string over the xml text.
Then change the scope from Application to User.
When I want to change the connection string, I use the following code.
// assign the path to use to the variable fullpath (or whatever)
string newConnection = String.Format("Provider=Microsoft.ACE.OLEDB.12.0;Data Source={0}", fullpath);
Properties.Settings.Default.HootConnectionString = newConnection;
Properties.Settings.Default.Save();
In my case, I have a global Dataset active, so I have to make that the data is reread by the tableadapter. And, of course, you'll have to add error control to make sure the database is still there.
You'll notice that this will not change what is displayed in Application Settings. Those are defaults.
This works for an Access database; so your mileage and requirements may vary.
EDIT: Caveat. As it works out, when installed, the connection string works well for opening and reading database content, but it complains about not having a connection string when trying to update a database.