You don't need mysqldump if you aren't using InnoDB. As long as you are moving to the same architecture, you can just tar up the database files and copy them to the new system: http://dev.mysql.com/doc/refman/6.0/en/upgrading-to-arch.html. It may even work for InnoDB, but that would require more checking.

This assumes, of course, that you are not really asking, "how can I move my database from one data center to the other without taking it down?" That, as the they say, is a horse of a completely different species...