Simply put, don't do it.
This case highlights why you should never use any business value, i.e. any 'real world values' for a Primary Key.
In your case I would recommend primary keys not be used for any other purposes. I recommend you add an extra column 'order' and then change THAT column in order to re-order the rows. That way your primary key and all the other records will not need to be touched.
This avoid the issue that your approach would need to change ALL the database records below the current record which seems like a really bad approach. Just imagine trying to undo that update ;)
Some more info here: https://stackoverflow.com/a/8777574/631619