Maybe this is what you want:

#!/usr/bin/perl

use strict;
use warnings;

close STDOUT;

open( STDOUT, '>', \( my $output ) )
    or die "Can't open in-memory file: $!";

print "Hello world!\n";  # prints to $output

print STDERR 'STDOUT: ' . $output;
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Output:

STDOUT: Hello world!
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