What I would do is:

open my $hold, '>&', STDOUT or die "Failed to dup STDOUT\n";
open STDOUT, '>', 'output.txt' or die "Failed to re-open STDOUT\n";

# later, if you want to restore STDOUT:
open STDOUT, '>&', $hold or die "Failed to restore STDOUT\n";
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The only line you really need is the second open. The first and the third opens are there only in case you want to restore STDOUT to its original state.