Probably the simplest thing would be to subclass BerkeleyDB::Hash and override the FETCH() and STORE() methods something like (untested):

package BerkeleyDB::Hash::CasePreserve;

sub FETCH {
  my( $self, $key ) = @_;

  unless( $self->EXISTS( $key ) ) {
    my $key_re = qr/\A$key\z/i;
    my $check = $self->FIRSTKEY( );
    do { 
      if( $check =~ $key_re ) {
        $key = $check;
        last;
      }
    } while( $check = $self->NEXTKEY( $check ) );
  }

  return $self->SUPER::FETCH( $key );
}
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Update: Added anchored $key_re.