A Variable::Magic solution:

use Cwd             qw( getcwd );
use Variable::Magic qw( cast wizard );

my $wiz = wizard(
   get => sub {
      ${ $_[0] } = getcwd();
   },
   set => sub {
      chdir( ${ $_[0] } )
         or die( "chdir `${ $_[0] }`: $!" );
   },
);

cast my $CD, $wiz;
[download]

With an alias:

use experimental qw( refaliasing declared_refs );

use Cwd             qw( getcwd );
use Variable::Magic qw( cast wizard );

my $wiz = wizard(
   get => sub {
      my \$sv = shift;
      $sv = getcwd();
   },
   set => sub {
      my \$sv = shift;
      chdir( $sv )
         or die( "chdir `$sv`: $!" );
   },
);

cast my $CD, $wiz;
[download]