replicate master/slave without disturbing master for dump
I would recommend Percona's Xtrabackup for this, especially since you mentioned all of your tables are InnoDB. From the page:


  Percona XtraBackup is designed to make backups a seamless procedure without disrupting the performance of the server in a production environment.


The tool will allow you to take a backup without locking innodb tables. It will do a lock to copy any MyISAM tables (such as the tables mysql in the mysql database) but those shouldn't take long.

I cannot tell you how long it will take on 400GB database, but it should do it without downtime.