All of the other responses have been good, but for another (and IMHO, a more C::A) way...
I would use the mode_param() accessor that can also take an anonymous sub.

sub setup {
  my $self = shift;
  $self->mode_param(\&_translate_old);
}

sub _translate_old {
  my $self = shift;
  my $query = $self->query();
  if( $query->param('page') {
    return $query->param('page');
  } elsif ( $query->param('stats') }
    return 'stats';
  } elsif( $query->param('new') {
    return 'new';
  }
}
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