I would set up a factory method in Searchable that is configured external to your program. Since you are already dealing with a database that is ideal. Set up a table with 2 columns (or more if you have a reason to) one the primary key lists the table names you want to have searchable, the second holds the name of the module to handle that table. Then the factory function would be something like this:

#called as Searchable->getTableHandler($table);
sub getTableHandler {
    my $class = shift;
    my $table = shift;

    #get $handlerClass from db

    eval "use $handlerClass;";
    #deal with errors

    return $handlerClass->new($table);
}
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The advantages of this is that you don't have to alter the main script any time you want to add a table, and there is only one place new tables and modules need to be added. Down sides are that it uses string eval to pull in the module at run time, that can cause delays as the compiler fires up again, and it risks that if someone gets some malicious code into your configuration you could have a serious problem.