We had a situation where a certain report needed to be accessed out of hours, when the report server was being refreshed. My solution was to include a drop-down list in the report called “Data Source”.

Then within the Data Source Properties I chose ‘build’ with a (temporary) static server name to get the login configured (which needs to be the same on both servers). Then amended the connection string by choosing ‘fx’ to construct something like this …

Note: Going forward, when working on reports with dynamic data sources I tend to change them back to ‘static’ and refresh the datasets before starting. Then put them back at the end.