Sort of depends on what is 'different' in you new tables. If the field names are the same, and just the data has changed, then you can Edit the Data Source and point it at the new tables. If they are not the same, but they're similar, then you are going to have to hunt down the errors and fix them. (Replace Reference is a handy tool for this.) The other option is to create a new connection and then Replace the old one with the new one.
It really comes down to how different the tables are. Which is going to take longer, fixing errors or rebuilding the dashboards.