It's pretty easy - all you have to do is open STDERR as a filehandle, directed to /dev/null:

#!/usr/bin/perl -w

use strict;

open (STDERR, "/dev/null");
select STDERR;
print "hi mum!";
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for example.

You might also want to read perlfaq8, including "How can I capture STDERR from an external command?", or type "perldoc -q STDERR".