This sounds promising.

From perl's core documentation: open

Here is a script that saves, redirects, and restores STDOUT and STDERR
+ using various methods:
    #!/usr/bin/perl
    open(my $oldout, ">&STDOUT")     or die "Can't dup STDOUT: $!";
    open(OLDERR,     ">&", \*STDERR) or die "Can't dup STDERR: $!";
    
    open(STDOUT, '>', "foo.out") or die "Can't redirect STDOUT: $!";
    open(STDERR, ">&STDOUT")     or die "Can't dup STDOUT: $!";
    
    select STDERR; $| = 1;  # make unbuffered
    select STDOUT; $| = 1;  # make unbuffered
    
    print STDOUT "stdout 1\n";  # this works for
    print STDERR "stderr 1\n";  # subprocesses too
    
    open(STDOUT, ">&", $oldout) or die "Can't dup \$oldout: $!";
    open(STDERR, ">&OLDERR")    or die "Can't dup OLDERR: $!";
    
    print STDOUT "stdout 2\n";
    print STDERR "stderr 2\n";
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