But considering that some folks have had problems having ex-CAI tix re-issued because the taxes are not always shown (and others have had no such problems, apparently) if you have time to have CAI make the change, you might avoid problems by doing so. A little gift to your agent might soothe any guilt you acquire in the process.
Looking at routing changes myself, I have to decide if I want to drive to LAX (basically an hour each way), Fedex tix to BA in Florida, or Fedex them back to CAI.