I'd have to test this out but isn't Class::DBI usually used in a module-2-table manner? If so, you could have something like this:

package MyModule::DBI;
use base 'Class::DBI';
MyModule::DBI->set_db(...);

...

package MyModule::Table;
use base 'MyModule::DBI'; 
MyModule::Table->table('table');

...

package MyModule::DB2_Table;
use base 'MyModule::DBI';
MyModule::DB2_Table->table( 'db2.table' );

# that should work depending on the security
# and access restrictions

....

my @db1_data = MyModule::Table->search( field => 'value' );
my @db2_data = MyModule::DB2_Table->search( field => 'value' );

...
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But then again, it's these types of situations that make me steer away from Class::DBI.