Best way to copy MS SQL (2000) database files to an external drive
Per the specific requirements of getting copies of the .mdf and .ldf files, you can simply stop the SQL Server service, copy the files, then start the SQL Server service.

The way to do it without downtime would be to take full backups, but then the other party would be required to restore the backups instead of just copying files.  This would be the preferred method in almost all cases, but if the other party doesn't want to manually restore 90 databases or take the time to automate the restoration, the file copy method is understandable.