If all tables are MyISAM I have good news !!!
A mysqldump, while it will work and is bitwise safer and conservative, is totally not required.
Each MyISAM table is comprised of three files: .frm, .MYD, .MYI.
You should be able to simply move the tables into a new database folder.
The information_schema database will automatically detect the presence of the three files and update itself (specifically update information_schema.schemata). Here is proof that can happen:
While MySQL is still running do the following
Once you run SHOW DATABASES; you should see thisisatest appear as a database. That's because information_schema automatically updated itself and registered /var/lib/mysql/thisisatest as a database. MyISAM tables will regsiter itself the same way (specifically update information_schema.tables). WARNING : THIS IS NOT POSSIBLE WITH InnoDB !!!