Just manually put in the new shipping amount, add a note if you want to and send. Only hit the 'recalculate' button if you put in a discount or extra charge percent (which is right above the recalculate button).
I've always found that the recalculate button just puts the invoice back to its original amount although that doesn't make a lot of sense. Just change the shipping amount and then click on preview to double check that it worked and then send it.