Can't do it with built-ins, but it's easy to create a function that can do it.

#!perl

use strict;
use warnings;

BEGIN {
    package Hash::Adjust;
    use Exporter::Shiny 'ha';
    
    sub _generate_ha {
        my ( $me, $name, undef, $opt ) = ( shift, @_ );
        
        my ( $aref, $bref ) = do {
            no strict 'refs';
            my $caller = $opt->{into};
            ( \${"$caller\::a"}, \${"$caller\::b"} );
        };
        
        return sub (&\%) {
            my ( $code, $hashref ) = ( @_ );
            @_ = ();
            my %tmp;
            while ( ( $$aref, $$bref ) = each %$hashref ) {
                &$code;
                $tmp{$$aref} = $$bref if defined $$aref;
            }
            %$hashref = %tmp;
        };
    }
};

use Hash::Adjust 'ha';
use Data::Dumper;

my %hash = ( FOO => 42, BAR => 666 );

ha {
    $a =~ s/O/o/g;
    ++$b;
} %hash;

print Dumper \%hash;
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The ha function is called like ha { CODE } %hash and modifies the keys and values of the hash. The code gets the key in $a and the value in $b; the same special global variables used by sort. If the code block sets $a = undef then that key-value pair will be removed from the hash.