Look into Expressions. They will do exactly what you need. Select your connection manager and about half way down the list of properties you will see "Expressions". Select it then click the ellipsis (...) next to it. From there you can set any property to an expression that will be evaluated at run time. In this case you want the ConnectionString property.

Note this is just one possible way of handling this. Another is Package Configurations. And for that matter you can pass properties for connections by using the /CONNECTION flag on dtexec.exe. If you want to go that route I recommend running dtexecui.exe and filling in the connection information (Connection Managers tab) then going to the Command Line tab to get the parameters to pass in.

I've used all of the above and none are terribly hard. Personally from what you said I would give Expressions a shot first though.