It's not that hard.

Either, instead of exists, use Data::Diver (by tye):

$ perl -Mstrict -MData::Diver=Dive -MData::Dumper -wE '
my $h; $h->{foo}->{bar}->{baz} = "qux";
say Dumper $h;
say Dive( $h, qw/ foo bar baz / ) ? 1 : 0;
say Dive( $h, qw/ foo NOT baz / ) ? 1 : 0;
say Dumper $h;
'
$VAR1 = {
          'foo' => {
                     'bar' => {
                                'baz' => 'qux'
                              }
                   }
        };

1
0
$VAR1 = {
          'foo' => {
                     'bar' => {
                                'baz' => 'qux'
                              }
                   }
        };
[download]

Or, if you want to use exists, just test for each level that you are not sure exists before going any deeper:

$ perl -Mstrict -MData::Dumper -wE '
my $h; $h->{foo}->{bar}->{baz} = "qux";
say Dumper $h;
say( (exists $h->{foo}->{bar}->{baz}) ? 1 : 0 );
say( (exists $h->{foo}->{NOT} && exists $h->{foo}->{NOT}->{baz}) ? 1 :
+ 0 );
say Dumper $h;
'
$VAR1 = {
          'foo' => {
                     'bar' => {
                                'baz' => 'qux'
                              }
                   }
        };

1
0
$VAR1 = {
          'foo' => {
                     'bar' => {
                                'baz' => 'qux'
                              }
                   }
        };
[download]