It really depends on how your container data is stored.
Under one of your container fields in File > Manage > Database, go to the "storage" tab. What are the settings there?
Also the settings under File > manage > containers
If we are talking about container fields where the "store a reference" option was used to insert each file, then yes, Replace Field Contents using the calculation option could be used to update the file references in each container field just as though it is a text field.
This is not simple and should be attempted on a back up copy of the file so that if it doesn't work you can revert to your original copy.
You can use GetAsText ( YourContainer field Here ) to see the text inside the container field in order to spot the text that serves as the file path to the file and see what kind of text "surgery" you need to do on it in order to achieve this update.