Adding at least one more field would be needed to "flag" selected records and this is a much better option than moving entire records from one table to another. But why would adding another field be a problem?
Could you please explain how to move an entire record from one table to the other?
I don't wish to help you do things in an extremely inefficient and possibly risky manner.
I don't see any need to move the record from one table to another if all you need to do is "flag" records. It's easy to add another field and store a value in the field to flag it. That really shouldn't be a problem for you or your database.