IO::Tee will do what you want. It's a little tricky to "cast" (C-speak) an IO::Tee object to a global handle, but this will do it. Perl 5.8x with PerlIO.

my $exitcode = do {
    use IO::Tee;

    open my $ef, '>>', '/path/to/stderr.txt' or die $!;
    open my $of, '>>', '/path/to/stdout.txt' or die $!;

    local *STDERR = *{IO::Tee->new('> /dev/tty', $ef)};
    local *STDOUT = *{IO::Tee->new('> /dev/tty', $of)};

    warn  scalar localtime;
    print scalar(localtime), "\n";

    warn  'Here I am!';
    print "Here, too!\n";

    system '/loc/of/perl', '/path/to/sample1.pl';
};
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As with any localized global variable, subroutines called from the local scope will honor the local value.