One short answer, wrap these two kinds of output in subroutines. Long answer:

sub output {
    my $text = shift;
    print STDOUT $text;
}

sub output_logged {
    my $text = shift;
    local *STDOUT;
    open(STDOUT, "| tee $filename") || die "Can't open pipe: $!";
    print STDOUT $text;
    close STDOUT;
}
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Other options include returning a filehandle from a subroutine and printing to that wherever you go. Remember, you can return a typeglob and capture it in a scalar.