There are a few more solutions that you could have used.

First and foremost, use a Safe. For example:

   use Safe;
   my $config = Safe->new;
   *{ $config->varglob($_) } = $handler{$_}
      for keys %handler;
   $ok = $config->reval( $cfg_str );
   # Or: $ok = $config->rdo( $config_source );
   $err = $@;
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When you are done, you can simply throw away the Safe object, and everything is totally cleaned up.

Secondly, (if using regular string eval, and not a Safe) you could have added the following to your $cfg_str:

join ";\n", map "local *$_ = \$handler{$_}", keys %handler;
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That would have cause the local to be undone the moment the string eval finished running.

Thirdly, you could have used recursion:

   local *handler_localizer = sub {
      if( my $name = each %handler ) {
         no strict 'refs';
         local *{$name} = $handler{$name};
         handler_localizer();
      } else {
         $ok = eval $cfg_str;
         $err = $@;
      }
   };
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But this is silly, when a Safe is so much simpler.